Test Paper Kinematics (Physics) JEE Notes | EduRev

JEE : Test Paper Kinematics (Physics) JEE Notes | EduRev

 Page 1


KINEMATICS- SET-1 
1. From a town, cars start at regular intervals of 30 s 
and run towards another town with constant speed 
of 60 km/h. At some point of time, all of the cars 
simultaneously have to reduce their speed to 40 
km/h due to bad weather conditions. What will 
become the time interval between arrivals of the 
cars at the second town during the bad weather? 
 (a) 20 s  (b) 30 s 
 (c) 40 s  (d) 45 s 
2. Sam used to walk to school every morning, and it 
takes him 20 minutes. Once on his way he realized 
that he had forgotten his homework, notebook at 
home. He knew that if he continued walking to 
school at the same speed, he would be there 8 
minutes before the bell, so he went back home for 
the notebook and arrived the school 10 minutes 
late. If he had walked all the way his usual speed, 
what fraction of the way to school had he covered 
at that moment when he turned back? 
 (a) 8/20   (b) 9/20 
 (c) 10/20  (d) 12/20 
3. A car moving at 160 km/h when passes the mark-A, 
driver applies brake and reduces its speed 
uniformly to 40 km/h at mark-C. The marks are 
spaced at equal distances along the road as shown 
below. 
 
Mark -A Mark -B Mark -C
 
 At which part of the track the car has instantaneous 
speed of 100 km/h? Neglect the size of the car. 
(a) At mark-B 
(b) Between mark-A and mark-B 
  (c) between mark-B and mark-C 
 (d) insufficient information to decide 
4. Two particles A and B starts from the same point 
and move in the positive x-direction. Their 
velocity-time relationships are shown in the 
following figures. What is the maximum separation 
between them during the time interval shown? 
 
Particle A
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 
Particle B
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 (a) 1.00 m  (b) 1.25 m 
 (c) 1.50 m  (d) 2.00 m 
5. A material particle is chasing the other one and 
both of them are moving on the same straight line. 
Their motion after they pass a particular point is 
recorded and the data obtained is shown by 
velocity-time graphs of the particles. How long 
after the start will the chase end? 
Velocity (m/s)
Time (s)
3 4
 
 (a) 4.0 s  (b) 6.0 s 
 (c) 12 s  (d) insufficient information 
6. Two cars A and B simultaneously start a race. 
Velocity of the car A varies with time according to 
the graph shown. It acquires a speed of 50 m/s few 
seconds before t = 100 s and then moves with this 
constant speed. Car B runs together with A to a 
place where both have velocity of 20 m/s, after this 
place car B moves with zero acceleration for one 
second and then follows velocity-time relationship 
identical to that of A with a delay of one second. In 
this way car B acquires the constant velocity one 
second after A acquires it. How much more 
distance ?s car A covers in the first 100 s? 
50
0
0 100
ts ()
v m s ( / )
 
 (a) ?s = 30 m  (b) ?s < 30 m 
 (c) ?s = 20 m  (d) insufficient information 
7. Two motorboats, which can move with velocities 
4.0 m/s and 6.0 m/s relative to water are going up-
stream. When the faster one overtakes the slower 
one, a buoy is dropped from the slower one. After 
lapse of some time both the boats turn back 
Page 2


KINEMATICS- SET-1 
1. From a town, cars start at regular intervals of 30 s 
and run towards another town with constant speed 
of 60 km/h. At some point of time, all of the cars 
simultaneously have to reduce their speed to 40 
km/h due to bad weather conditions. What will 
become the time interval between arrivals of the 
cars at the second town during the bad weather? 
 (a) 20 s  (b) 30 s 
 (c) 40 s  (d) 45 s 
2. Sam used to walk to school every morning, and it 
takes him 20 minutes. Once on his way he realized 
that he had forgotten his homework, notebook at 
home. He knew that if he continued walking to 
school at the same speed, he would be there 8 
minutes before the bell, so he went back home for 
the notebook and arrived the school 10 minutes 
late. If he had walked all the way his usual speed, 
what fraction of the way to school had he covered 
at that moment when he turned back? 
 (a) 8/20   (b) 9/20 
 (c) 10/20  (d) 12/20 
3. A car moving at 160 km/h when passes the mark-A, 
driver applies brake and reduces its speed 
uniformly to 40 km/h at mark-C. The marks are 
spaced at equal distances along the road as shown 
below. 
 
Mark -A Mark -B Mark -C
 
 At which part of the track the car has instantaneous 
speed of 100 km/h? Neglect the size of the car. 
(a) At mark-B 
(b) Between mark-A and mark-B 
  (c) between mark-B and mark-C 
 (d) insufficient information to decide 
4. Two particles A and B starts from the same point 
and move in the positive x-direction. Their 
velocity-time relationships are shown in the 
following figures. What is the maximum separation 
between them during the time interval shown? 
 
Particle A
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 
Particle B
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 (a) 1.00 m  (b) 1.25 m 
 (c) 1.50 m  (d) 2.00 m 
5. A material particle is chasing the other one and 
both of them are moving on the same straight line. 
Their motion after they pass a particular point is 
recorded and the data obtained is shown by 
velocity-time graphs of the particles. How long 
after the start will the chase end? 
Velocity (m/s)
Time (s)
3 4
 
 (a) 4.0 s  (b) 6.0 s 
 (c) 12 s  (d) insufficient information 
6. Two cars A and B simultaneously start a race. 
Velocity of the car A varies with time according to 
the graph shown. It acquires a speed of 50 m/s few 
seconds before t = 100 s and then moves with this 
constant speed. Car B runs together with A to a 
place where both have velocity of 20 m/s, after this 
place car B moves with zero acceleration for one 
second and then follows velocity-time relationship 
identical to that of A with a delay of one second. In 
this way car B acquires the constant velocity one 
second after A acquires it. How much more 
distance ?s car A covers in the first 100 s? 
50
0
0 100
ts ()
v m s ( / )
 
 (a) ?s = 30 m  (b) ?s < 30 m 
 (c) ?s = 20 m  (d) insufficient information 
7. Two motorboats, which can move with velocities 
4.0 m/s and 6.0 m/s relative to water are going up-
stream. When the faster one overtakes the slower 
one, a buoy is dropped from the slower one. After 
lapse of some time both the boats turn back 
KINEMATICS- SET-1 
simultaneously and move at the same speeds 
relative to the water as before. Their engines are 
switched off when they reach the buoy again. If the 
maximum separation between the boats is 200 m 
after the buoy is dropped and water flow velocity is 
1.5 m/s, find the distance between the two places 
where the boats meet the buoy. 
 (a) 75 m  (b) 150 m 
 (c) 300 m  (d) 350 m 
8. Two students start running on a circular track from 
the same place at the same time and in two minutes 
one of them completes three and other four 
revolutions. Due to thick vegetation in circular area, 
each of the boys can see only one third of the track 
at a time. How long during their run they will 
remain visible to each other? 
 
 (a) 20 s   (b) 40 s 
 (c) 80 s   (d) 160 s 
9. Three ants A, B and C initially rest on the vertices 
of an equilateral triangle on a large horizonal 
tabletop. The ants A and B can crawl with constant 
velocities 
A
v
?
 and 
B
v
?
 in any direction. Which of 
the following inequalities the speed of the third ant 
C must satisfy to preserve equilateral shape of the 
triangle? 
 (a) v
C
 < 0.5 (v
A
 + v
B
) (b) v
C
 = 0.5 (v
A
 + v
B
) 
 (c) v
C
 <  v
A
 + v
B
 (d) v
C
 = v
A
 + v
B
 
10. A body experiences a drag force proportional to its 
speed, when it moves in constant water. A student 
drops several identical stones one by one from 
different heights into a deep lake and for each 
stone, he prepares graphs between v in water and 
time t. Having studied all of them, he finds that 
they can be divided into the following three 
categories. 
 
v
v
0
t
  
 
v
v
0
t
 
 
v
v
0
t
  
  
 Which of the following explanations appear 
reasonable? 
 (a) the first graph shows what happens when the 
ball is dropped from a small height, and the second 
shows what happens when it is dropped from a 
large height. 
 (b) The first graph shows what happens when the 
ball is dropped from a large height, and the second 
shows what happens when it is dropped from a 
small height. 
 (c) The third graph tells the possibility only when 
the stone is dropped from such a height that it 
acquires the speed v
0
 at the instant it enters the 
water. 
 (d) The third graph is not possible. 
11. On a road going out of a city, the last traffic light 
glows green for 1.0 min and red for 2.0 min. After 
the traffic light, the road is straight and vehicles run 
at their constant speeds. This mode of operation of 
traffic lights causes the vehicles come out off the 
city in groups i.e., when traffic light is green a 
group of vehicles comes out and then next group 
during the next green signal and so on. Speeds of 
vehicles in a group lie in the range from 60 to 80 
km/h. Some distance away from the traffic light, 
the groups will become indistinguishable. Assume 
that the vehicles acquires their constant speed in 
negligible time and mark the correct statement or 
statements. 
 (a) at distance 4.0 km from the traffic light, the 
groups become indistinguishable. 
 (b) at distance 8.0 km from the traffic light, the 
group become indistinguishable. 
 (c) wider is the range of speed; longer is the 
distance where groups become indistinguishable. 
 (d) larger is the number of fast moving vehicles, 
shorter is the distance where groups become 
indistinguishable. 
Page 3


KINEMATICS- SET-1 
1. From a town, cars start at regular intervals of 30 s 
and run towards another town with constant speed 
of 60 km/h. At some point of time, all of the cars 
simultaneously have to reduce their speed to 40 
km/h due to bad weather conditions. What will 
become the time interval between arrivals of the 
cars at the second town during the bad weather? 
 (a) 20 s  (b) 30 s 
 (c) 40 s  (d) 45 s 
2. Sam used to walk to school every morning, and it 
takes him 20 minutes. Once on his way he realized 
that he had forgotten his homework, notebook at 
home. He knew that if he continued walking to 
school at the same speed, he would be there 8 
minutes before the bell, so he went back home for 
the notebook and arrived the school 10 minutes 
late. If he had walked all the way his usual speed, 
what fraction of the way to school had he covered 
at that moment when he turned back? 
 (a) 8/20   (b) 9/20 
 (c) 10/20  (d) 12/20 
3. A car moving at 160 km/h when passes the mark-A, 
driver applies brake and reduces its speed 
uniformly to 40 km/h at mark-C. The marks are 
spaced at equal distances along the road as shown 
below. 
 
Mark -A Mark -B Mark -C
 
 At which part of the track the car has instantaneous 
speed of 100 km/h? Neglect the size of the car. 
(a) At mark-B 
(b) Between mark-A and mark-B 
  (c) between mark-B and mark-C 
 (d) insufficient information to decide 
4. Two particles A and B starts from the same point 
and move in the positive x-direction. Their 
velocity-time relationships are shown in the 
following figures. What is the maximum separation 
between them during the time interval shown? 
 
Particle A
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 
Particle B
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 (a) 1.00 m  (b) 1.25 m 
 (c) 1.50 m  (d) 2.00 m 
5. A material particle is chasing the other one and 
both of them are moving on the same straight line. 
Their motion after they pass a particular point is 
recorded and the data obtained is shown by 
velocity-time graphs of the particles. How long 
after the start will the chase end? 
Velocity (m/s)
Time (s)
3 4
 
 (a) 4.0 s  (b) 6.0 s 
 (c) 12 s  (d) insufficient information 
6. Two cars A and B simultaneously start a race. 
Velocity of the car A varies with time according to 
the graph shown. It acquires a speed of 50 m/s few 
seconds before t = 100 s and then moves with this 
constant speed. Car B runs together with A to a 
place where both have velocity of 20 m/s, after this 
place car B moves with zero acceleration for one 
second and then follows velocity-time relationship 
identical to that of A with a delay of one second. In 
this way car B acquires the constant velocity one 
second after A acquires it. How much more 
distance ?s car A covers in the first 100 s? 
50
0
0 100
ts ()
v m s ( / )
 
 (a) ?s = 30 m  (b) ?s < 30 m 
 (c) ?s = 20 m  (d) insufficient information 
7. Two motorboats, which can move with velocities 
4.0 m/s and 6.0 m/s relative to water are going up-
stream. When the faster one overtakes the slower 
one, a buoy is dropped from the slower one. After 
lapse of some time both the boats turn back 
KINEMATICS- SET-1 
simultaneously and move at the same speeds 
relative to the water as before. Their engines are 
switched off when they reach the buoy again. If the 
maximum separation between the boats is 200 m 
after the buoy is dropped and water flow velocity is 
1.5 m/s, find the distance between the two places 
where the boats meet the buoy. 
 (a) 75 m  (b) 150 m 
 (c) 300 m  (d) 350 m 
8. Two students start running on a circular track from 
the same place at the same time and in two minutes 
one of them completes three and other four 
revolutions. Due to thick vegetation in circular area, 
each of the boys can see only one third of the track 
at a time. How long during their run they will 
remain visible to each other? 
 
 (a) 20 s   (b) 40 s 
 (c) 80 s   (d) 160 s 
9. Three ants A, B and C initially rest on the vertices 
of an equilateral triangle on a large horizonal 
tabletop. The ants A and B can crawl with constant 
velocities 
A
v
?
 and 
B
v
?
 in any direction. Which of 
the following inequalities the speed of the third ant 
C must satisfy to preserve equilateral shape of the 
triangle? 
 (a) v
C
 < 0.5 (v
A
 + v
B
) (b) v
C
 = 0.5 (v
A
 + v
B
) 
 (c) v
C
 <  v
A
 + v
B
 (d) v
C
 = v
A
 + v
B
 
10. A body experiences a drag force proportional to its 
speed, when it moves in constant water. A student 
drops several identical stones one by one from 
different heights into a deep lake and for each 
stone, he prepares graphs between v in water and 
time t. Having studied all of them, he finds that 
they can be divided into the following three 
categories. 
 
v
v
0
t
  
 
v
v
0
t
 
 
v
v
0
t
  
  
 Which of the following explanations appear 
reasonable? 
 (a) the first graph shows what happens when the 
ball is dropped from a small height, and the second 
shows what happens when it is dropped from a 
large height. 
 (b) The first graph shows what happens when the 
ball is dropped from a large height, and the second 
shows what happens when it is dropped from a 
small height. 
 (c) The third graph tells the possibility only when 
the stone is dropped from such a height that it 
acquires the speed v
0
 at the instant it enters the 
water. 
 (d) The third graph is not possible. 
11. On a road going out of a city, the last traffic light 
glows green for 1.0 min and red for 2.0 min. After 
the traffic light, the road is straight and vehicles run 
at their constant speeds. This mode of operation of 
traffic lights causes the vehicles come out off the 
city in groups i.e., when traffic light is green a 
group of vehicles comes out and then next group 
during the next green signal and so on. Speeds of 
vehicles in a group lie in the range from 60 to 80 
km/h. Some distance away from the traffic light, 
the groups will become indistinguishable. Assume 
that the vehicles acquires their constant speed in 
negligible time and mark the correct statement or 
statements. 
 (a) at distance 4.0 km from the traffic light, the 
groups become indistinguishable. 
 (b) at distance 8.0 km from the traffic light, the 
group become indistinguishable. 
 (c) wider is the range of speed; longer is the 
distance where groups become indistinguishable. 
 (d) larger is the number of fast moving vehicles, 
shorter is the distance where groups become 
indistinguishable. 
KINEMATICS- SET-1 
12. A boy takes 60 minutes to swim across a river, if 
his goal is to minimize time and he takes 180 
minutes, if his goal is to minimize to zero the 
distance that he is being carried downstream. In 
both these efforts, the boy swims with the same 
speed relative to river currents. Which of the 
following statements can be true? 
 (a) the boy can swim in still water faster than the 
river current. 
 (b) the boy cannot swim in still water faster than 
the river current. 
 (c) if river width is 3v2 km, speed of the river flow 
is 4 km/h. 
 (d) if he crosses 3v2 km wide river in 60v2 min, he 
will be carried v2 km downstream. 
13. A wax bar B rests between a wedge A and a 
vertical wall as shown in the figure. The wedge 
starts moving towards the wall with a constant 
acceleration of 0.5 mm/s
2
, and at the same instant 
heat given to the wall starts melting 1.0 mm length 
of the wax bar per second. The bar always remains 
horizontal. Use satisfactorily approximate value sin 
37° = 3/5. 
Heat
37°
A
B
 
 Which of the following descriptions suits the above 
physical situation? 
 (a) the bar first moves downwards and then 
upwards 
 (b) the bar stops momentarily after 2 seconds from 
the beginning. 
 (c) modulus of displacement of the bar in the first 
four seconds is 1.5 mm 
 (d) distance travelled by the bar in the first four 
seconds is 1.5 mm 
14. A model rocket fired from the ground ascends with 
constant upward acceleration. After 1.0 s from 
firing a small bolt is dropped from the rocket and 
after 5.0 s from firing, its fuel is then finished. The 
bolt strikes the ground after 2.0 s from the instant it 
was dropped. Acceleration due to gravity is g = 10 
m/s
2
. 
 (a) acceleration of the rocket while running on its 
fuel is 8.0 m/s
2
. 
 (b) rocket was at height 100 m above the ground 
when its fuel was finished. 
 (c) maximum speed of the rocket during its flight is 
40 m/s 
 (d) total airtime of the rocket is 15 s 
15. Area between velocity-time graph and the time axis 
equals to displacement. Use this fact to find 
expression for average velocity and suggest suitable 
match between the two rows. 
 Row-I 
 
v
2
v
1
T
(a)
 
v
2
v
1
T/2
(b)
T
 
 
v
2
v
1
34 T/
(c)
T
v
2
v
1
T/4
(d)
T
 
 Row-II 
 (p) 
12 av
v v v ?? (q) 
12
3
4
av
vv
v
?
? 
 (r)   
12
3
4
av
vv
v
?
? (s) 
12
2
av
vv
v
?
? 
16. Component of a vector along and perpendicular to 
the position vector are known as the radial 
component and transverse components respectively. 
A particle is projected horizontally from the top of 
a tower. Assume acceleration due to gravity g 
uniform and take the origin of the coordinate 
system at the point of projection. 
 Column-I 
 (p) radial component of velocity 
 (q) transverse component of velocity 
 (r) radial component of acceleration 
 (s) transverse component of acceleration 
 Column-II 
 (a) always increases (b) always decreases 
 (c) first increases then decreases 
 (d) first decreases then increases 
For Problems (17-20) 
A stone is dropped from the top of a tower. Before it hits 
the ground another stone is dropped. Assuming the 
Page 4


KINEMATICS- SET-1 
1. From a town, cars start at regular intervals of 30 s 
and run towards another town with constant speed 
of 60 km/h. At some point of time, all of the cars 
simultaneously have to reduce their speed to 40 
km/h due to bad weather conditions. What will 
become the time interval between arrivals of the 
cars at the second town during the bad weather? 
 (a) 20 s  (b) 30 s 
 (c) 40 s  (d) 45 s 
2. Sam used to walk to school every morning, and it 
takes him 20 minutes. Once on his way he realized 
that he had forgotten his homework, notebook at 
home. He knew that if he continued walking to 
school at the same speed, he would be there 8 
minutes before the bell, so he went back home for 
the notebook and arrived the school 10 minutes 
late. If he had walked all the way his usual speed, 
what fraction of the way to school had he covered 
at that moment when he turned back? 
 (a) 8/20   (b) 9/20 
 (c) 10/20  (d) 12/20 
3. A car moving at 160 km/h when passes the mark-A, 
driver applies brake and reduces its speed 
uniformly to 40 km/h at mark-C. The marks are 
spaced at equal distances along the road as shown 
below. 
 
Mark -A Mark -B Mark -C
 
 At which part of the track the car has instantaneous 
speed of 100 km/h? Neglect the size of the car. 
(a) At mark-B 
(b) Between mark-A and mark-B 
  (c) between mark-B and mark-C 
 (d) insufficient information to decide 
4. Two particles A and B starts from the same point 
and move in the positive x-direction. Their 
velocity-time relationships are shown in the 
following figures. What is the maximum separation 
between them during the time interval shown? 
 
Particle A
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 
Particle B
1.00 m/s
2.00 m/s
1.00 s 2.00 s
 
 (a) 1.00 m  (b) 1.25 m 
 (c) 1.50 m  (d) 2.00 m 
5. A material particle is chasing the other one and 
both of them are moving on the same straight line. 
Their motion after they pass a particular point is 
recorded and the data obtained is shown by 
velocity-time graphs of the particles. How long 
after the start will the chase end? 
Velocity (m/s)
Time (s)
3 4
 
 (a) 4.0 s  (b) 6.0 s 
 (c) 12 s  (d) insufficient information 
6. Two cars A and B simultaneously start a race. 
Velocity of the car A varies with time according to 
the graph shown. It acquires a speed of 50 m/s few 
seconds before t = 100 s and then moves with this 
constant speed. Car B runs together with A to a 
place where both have velocity of 20 m/s, after this 
place car B moves with zero acceleration for one 
second and then follows velocity-time relationship 
identical to that of A with a delay of one second. In 
this way car B acquires the constant velocity one 
second after A acquires it. How much more 
distance ?s car A covers in the first 100 s? 
50
0
0 100
ts ()
v m s ( / )
 
 (a) ?s = 30 m  (b) ?s < 30 m 
 (c) ?s = 20 m  (d) insufficient information 
7. Two motorboats, which can move with velocities 
4.0 m/s and 6.0 m/s relative to water are going up-
stream. When the faster one overtakes the slower 
one, a buoy is dropped from the slower one. After 
lapse of some time both the boats turn back 
KINEMATICS- SET-1 
simultaneously and move at the same speeds 
relative to the water as before. Their engines are 
switched off when they reach the buoy again. If the 
maximum separation between the boats is 200 m 
after the buoy is dropped and water flow velocity is 
1.5 m/s, find the distance between the two places 
where the boats meet the buoy. 
 (a) 75 m  (b) 150 m 
 (c) 300 m  (d) 350 m 
8. Two students start running on a circular track from 
the same place at the same time and in two minutes 
one of them completes three and other four 
revolutions. Due to thick vegetation in circular area, 
each of the boys can see only one third of the track 
at a time. How long during their run they will 
remain visible to each other? 
 
 (a) 20 s   (b) 40 s 
 (c) 80 s   (d) 160 s 
9. Three ants A, B and C initially rest on the vertices 
of an equilateral triangle on a large horizonal 
tabletop. The ants A and B can crawl with constant 
velocities 
A
v
?
 and 
B
v
?
 in any direction. Which of 
the following inequalities the speed of the third ant 
C must satisfy to preserve equilateral shape of the 
triangle? 
 (a) v
C
 < 0.5 (v
A
 + v
B
) (b) v
C
 = 0.5 (v
A
 + v
B
) 
 (c) v
C
 <  v
A
 + v
B
 (d) v
C
 = v
A
 + v
B
 
10. A body experiences a drag force proportional to its 
speed, when it moves in constant water. A student 
drops several identical stones one by one from 
different heights into a deep lake and for each 
stone, he prepares graphs between v in water and 
time t. Having studied all of them, he finds that 
they can be divided into the following three 
categories. 
 
v
v
0
t
  
 
v
v
0
t
 
 
v
v
0
t
  
  
 Which of the following explanations appear 
reasonable? 
 (a) the first graph shows what happens when the 
ball is dropped from a small height, and the second 
shows what happens when it is dropped from a 
large height. 
 (b) The first graph shows what happens when the 
ball is dropped from a large height, and the second 
shows what happens when it is dropped from a 
small height. 
 (c) The third graph tells the possibility only when 
the stone is dropped from such a height that it 
acquires the speed v
0
 at the instant it enters the 
water. 
 (d) The third graph is not possible. 
11. On a road going out of a city, the last traffic light 
glows green for 1.0 min and red for 2.0 min. After 
the traffic light, the road is straight and vehicles run 
at their constant speeds. This mode of operation of 
traffic lights causes the vehicles come out off the 
city in groups i.e., when traffic light is green a 
group of vehicles comes out and then next group 
during the next green signal and so on. Speeds of 
vehicles in a group lie in the range from 60 to 80 
km/h. Some distance away from the traffic light, 
the groups will become indistinguishable. Assume 
that the vehicles acquires their constant speed in 
negligible time and mark the correct statement or 
statements. 
 (a) at distance 4.0 km from the traffic light, the 
groups become indistinguishable. 
 (b) at distance 8.0 km from the traffic light, the 
group become indistinguishable. 
 (c) wider is the range of speed; longer is the 
distance where groups become indistinguishable. 
 (d) larger is the number of fast moving vehicles, 
shorter is the distance where groups become 
indistinguishable. 
KINEMATICS- SET-1 
12. A boy takes 60 minutes to swim across a river, if 
his goal is to minimize time and he takes 180 
minutes, if his goal is to minimize to zero the 
distance that he is being carried downstream. In 
both these efforts, the boy swims with the same 
speed relative to river currents. Which of the 
following statements can be true? 
 (a) the boy can swim in still water faster than the 
river current. 
 (b) the boy cannot swim in still water faster than 
the river current. 
 (c) if river width is 3v2 km, speed of the river flow 
is 4 km/h. 
 (d) if he crosses 3v2 km wide river in 60v2 min, he 
will be carried v2 km downstream. 
13. A wax bar B rests between a wedge A and a 
vertical wall as shown in the figure. The wedge 
starts moving towards the wall with a constant 
acceleration of 0.5 mm/s
2
, and at the same instant 
heat given to the wall starts melting 1.0 mm length 
of the wax bar per second. The bar always remains 
horizontal. Use satisfactorily approximate value sin 
37° = 3/5. 
Heat
37°
A
B
 
 Which of the following descriptions suits the above 
physical situation? 
 (a) the bar first moves downwards and then 
upwards 
 (b) the bar stops momentarily after 2 seconds from 
the beginning. 
 (c) modulus of displacement of the bar in the first 
four seconds is 1.5 mm 
 (d) distance travelled by the bar in the first four 
seconds is 1.5 mm 
14. A model rocket fired from the ground ascends with 
constant upward acceleration. After 1.0 s from 
firing a small bolt is dropped from the rocket and 
after 5.0 s from firing, its fuel is then finished. The 
bolt strikes the ground after 2.0 s from the instant it 
was dropped. Acceleration due to gravity is g = 10 
m/s
2
. 
 (a) acceleration of the rocket while running on its 
fuel is 8.0 m/s
2
. 
 (b) rocket was at height 100 m above the ground 
when its fuel was finished. 
 (c) maximum speed of the rocket during its flight is 
40 m/s 
 (d) total airtime of the rocket is 15 s 
15. Area between velocity-time graph and the time axis 
equals to displacement. Use this fact to find 
expression for average velocity and suggest suitable 
match between the two rows. 
 Row-I 
 
v
2
v
1
T
(a)
 
v
2
v
1
T/2
(b)
T
 
 
v
2
v
1
34 T/
(c)
T
v
2
v
1
T/4
(d)
T
 
 Row-II 
 (p) 
12 av
v v v ?? (q) 
12
3
4
av
vv
v
?
? 
 (r)   
12
3
4
av
vv
v
?
? (s) 
12
2
av
vv
v
?
? 
16. Component of a vector along and perpendicular to 
the position vector are known as the radial 
component and transverse components respectively. 
A particle is projected horizontally from the top of 
a tower. Assume acceleration due to gravity g 
uniform and take the origin of the coordinate 
system at the point of projection. 
 Column-I 
 (p) radial component of velocity 
 (q) transverse component of velocity 
 (r) radial component of acceleration 
 (s) transverse component of acceleration 
 Column-II 
 (a) always increases (b) always decreases 
 (c) first increases then decreases 
 (d) first decreases then increases 
For Problems (17-20) 
A stone is dropped from the top of a tower. Before it hits 
the ground another stone is dropped. Assuming the 
KINEMATICS- SET-1 
stones stick to the ground after hit, the separation 
(s) between them is plotted against time (t). Portion 
OA and BC of the graph are parabolic, while 
portion AB is a straight line. Acceleration due to 
gravity is 10 m/s
2
. 
s(m)
10
O
1 2 3 4 t(s)
C
B
A
20
40
 
17. The second stone is dropped 
 (a) 1s after the first 
 (b) 1.5 s after the first 
 (c) 2 s after the first 
 (d) 3 s after the first 
18. The height of the tower is 
 (a) 25 m (b) 30 m 
 (c) 40 m (d) 45 m 
19. When the first stone hits the ground, the second 
stone was moving with 
 (a) 10 m/s at 40 above the ground 
 (b) 10 m/s at 25 above the ground 
 (c) 20 m/s at 20 above the ground 
 (d) 20 m/s at 25 above the ground 
20. Which of the following equations can be used to 
represent the separation as function of time is 
 (a) s = 5t
2
; 0 = t = 1  
 (b) s = 10t; 1 = t = 3 
 (c) 45 –  5(t-1)
2
; 3 = t = 4 
 (d) all of the above 
 
ANSWERS 
 
1.[d]  2.[b] 3.[c] 4.[b] 5.[b] 
6.[a]  7.[c] 8.[b] 9.[d] 10.[b,c]  
11.[b]  12.[a,c,d] 13.[a,b,d] 
14.[a,b,c,d] 
15. [p – a,d] [q – a,d] 
 [r – a,b] [s – a,c] 
16. [p – a]  [q – a] 
 [r – a]  [s – b] 
17.[a]  18.[d]  19.[d]  20.[d] 
 
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