Q.1. m/s2 is the SI unit of -
(a) distance
(b) displacement
(c) velocity
(d) acceleration
Ans: a
Solution: The meter per second squared (symbolized m/s2 or m/sec2) is the Standard International ( SI ) unit of acceleration vector magnitude. This quantity can be defined in either of two senses: average or instantaneous.
Q.2. A car goes from a town A to another town B with a speed of 40 km/h and returns back to the town A with a speed of 60 km/h. The average speed of the car during the complete journey is -
(a) 48 km/h
(b) 50 km/h
(c) zero
(d) none of these
Ans: a
Solution: Let the total distance travelled to and fro be d
Speed while going from town A to town B = 40 km/hr
Speed while coming back from town B to town A = 60 km/hr
Time taken to go to town B, t
1 = Distance/Speed
Time taken to return to town A,
Average speed = Total Distance/Total Time
= 9600/200
= 48 km/hr
Q.3. The rate of change of displacement with time is called -
(a) speed
(b) velocity
(c) acceleration
(d) retardation
Ans: b
Solution: ds/dt = v
Rate of change of displacement with time is velocity.
Q.4. The initial velocity of a body is u. It is under uniform acceleration a. Its velocity v at any time t is given by -
(a) v = u + at2
(b) v = u + ½ at2
(c) v = u + at
(d) v = u
Ans: c
Solution: Velocity of the body after time t with an acceleration a is given by: V = u + at
Q.5. The distance covered in time t by a body having initial velocity u and having a uniform acceleration a is given by s = ut + ½ at2. This result follows from -
(a) Newton’s first law
(b) Newton’s second law
(c) Newton’s third law
(d) None of these
Ans: d
Solution: Newton's Laws of motion are related to the behaviour of motion of objects on the effect of external force. Derivation of distance covered by a body cannot be concluded from them.
s = ut + ½ at2 follows from basic definitions in kinematics.
Q.6. A ball is thrown vertically upwards. It rises to a height of 50 m and comes back to the thrower,
(a) the total distance covered by the ball is zero
(b) the net displacement of the ball is zero
(c) the displacement is 100 m
(d) none of these
Ans: b
Solution:
As distance describes the path along which the ball moved. The distance travelled will be 100m.
The displacement of the ball from the initial point to the height is +50m and the displacement from the height to the thrower is -50m.
As the direction of both movements are opposite, the magnitude cancels. So the net displacement will be zero.
Q.7. In 12 minutes a car whose speed is 35 km/h travels a distance of
(a) 7 km
(b) 3.5 km
(c) 14 km
(d) 28 km
Ans: a
Solution: Speed = 35 km/hr = 35 × ( 5 / 18 ) = 9.72 m/s
time = 12 min = ( 12 × 60 ) = 720 s
Distance = speed × time = 9.72 × 720 = 7000 m = 7 km.
Q.8. When a graph of one quantity versus another results in a straight line, the quantities are
(a) both constant
(b) equal
(c) directly proportional
(d) inversely proportional
Ans: c
Solution: When a graph of one quantity versus another results in a straight line the quantities are then they are directly proportional to each other.
Q.9. A body moving along a straight line at 20 m/s undergoes an acceleration of 4 m/s2. After two seconds its speed will be -
(a) -8 m/s
(b) 12 m/s
(c) 16 m/s
(d) 28 m/s
Ans: d
Solution: U= 20 m/s
a= 4 m/s2
v = u + at = 20 + 4 × 2 = 28 m/s
Q.10. A car increases its speed from 20 km/h to 30 km/h in 10 seconds. Its acceleration is
(a) 30 m/s2
(b) 3 m/s2
(c) 18 m/s2
(d) 0.83 m/s2
Ans: d
Solution: Change in velocity = Δv = 30 - 20 =10 km/h
Time involved = 10 s = 10/60 minutes = (10/60) ÷ 60 h = 1/360 h
Acceleration = a = Δv/Δt = (10 km/h) ÷ (1/360 h) = 10 × 360 km/h² = 3600 km/h²
a = 3600 × 1000 m ÷ (3600 s)2
a = 1000 m ÷ 3600 s2
a = 10/36 m/s2
a = 0.28 m/s2
Q.11. A body whose speed is constant
(a) must be accelerated
(b) might be accelerated
(c) has a constant velocity
(d) can not be accelerated
Ans: b
Solution: If a body with constant speed is travelling in the same direction(i.e. it is not changing its direction) then its velocity is constant and so its acceleration will be zero. But if the object is changing its direction then its velocity is also changing and so it possesses the acceleration.
Q.12. When the distance that an object travels is directly proportional to the length of time it is said to travel with
(a) zero velocity
(b) constant speed
(c) constant acceleration
(d) uniform velocity
Ans: b
Solution:
When the distance travelled by an object is directly proportional to the time, it is said to travel with constant speed.
An object is said to be in uniform speeds when the object travels equal distances in equal interval of time.
Uniform and non-uniform motions of objects can be shown through graphs.
The speed of an object can be determined from the distance-time graph.
The velocity of an object is the displacement per unit time.
The acceleration of a moving object is the rate of change in velocity.
Q.13. A particle moves with uniform positive acceleration. Its velocity-time graph will be
(a) a straight line parallel to the time axis
(b) a straight line inclined at an obtuse angle to the time axis
(c) a straight line inclined at an acute angle to the time axis
(d) none of these
Ans: c
Solution: An object moves with uniform positive acceleration. Then, its velocity-time graph will be a straight line inclined at the acute angle to the time axis.
Q.14. The slope of speed-time graph gives
(a) speed
(b) velocity
(c) acceleration
(d) momentum
Ans: c
Solution: A sloping line on a speed-time graph represents an acceleration. The sloping line shows that the speed of the object is changing. The object is either speeding up or slowing down. If the line slopes upward from left to right, this means the object is speeding up.
Q.15. A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance s1 in the first 10 seconds and distance s2 in the next 10 seconds then,
(a) s2 = s1
(b) s2 = 2s1
(c) s2 = 3s1
(d) s2 = 4s1
Ans: c
Solution: since, we know that
S = ut + 1/2a(t2)
initial velocity u = 0 m/sec
since particle starts from rest. S1=1/2a(t2)
S1 = 1/2a(102)
S1 = 50a -------------------- (1)
now initial velocity for S2 is the final velocity of s1
let final velocity of S1 = initial velocity of S2 = v
so, v = u +at
v = at
v = 10a (because here u = 0 and t = 10)
now S2 = ut + 1/2a(t2)
S2 = (10a)10 + 1/2a(102)
S2 = 100a + 50a
S2 = 150a -------------------(2)
now
(2)/(1) = S1/S2
S1/S2 = 50a/150a
S2 = 3S1
Q.16. In which of the following cases the object does not possess an acceleration or retardation when it moves in
(a) upward direction with decreasing speed
(b) downward direction with increasing speed
(c) with constant speed along circular path
(d) with constant speed along horizontal path
Ans: d
Solution: When an object is moving with constant velocity along horizontal direction then change in velocity should always be zero. Hence, the object does not possess an acceleration or retardation when it moves with constant speed along horizontal direction.
Q.17. A person travels distance πR along the circumference of a circle of radius R. Displacement of the person is
(a) R
(b) 2R
(c) 2πR
(d) zero
Ans: b
Solution: Here, the displacement is equal to diameter or 2*radius and given radius of circle is R. Therefore, the Displacement of the person is 2R.
Q.18. The velocity of an object is directly proportional to the time elapsed. The object has
(a) uniform speed
(b) uniform velocity
(c) uniform acceleration
(d) variable acceleration
Ans: c
Solution: As free fall is an example of uniform accelerated motion, The velocity of an object is directly proportional to the time elapsed. The object has uniform acceleration.