JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

JEE: JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

The document JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is a part of the JEE Course Physics For JEE.
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Q.1.  A particle is moving along the x-axis, with its coordinate as a function of time given by x(t) =10+ 8t - 3t2. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t) = 5 - 8t3. At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as √v. Then v (in m/s) is ______.    [2020]
Ans.
580
Solution: Given that
 x(t) =10+ 8t - 3t2, y(t) = 5 - 8t3 
So,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
At t = 1 s, we have
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Relative velocity of second particle with respect to first particle is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q.2. A particle moves such that it's position vector is JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE where ω is a constant and t is time. Then which of the following statements is true for the velocity JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE and acceleration  JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE of the particle.
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is perpendicular to JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEEis directed away from the origin.
(2) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE both are perpendicular to JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE both are parallel to JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is perpendicular to  JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is directed towards the origin.
Ans:
(4)
Solution: Given that
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
So,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
and
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Since, JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is perpendicular to JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
And JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE had opposite direction to  JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE or antiparallel to  JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE that is, directed towards the origin.

Q.3. A ball is dropped from the top of a 100 m high tower on a planet. In the last (1/2)s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in m/s2) near the surface on that planet is _______.
Ans.
8
Solution: Given that
u = 0 m/s, H = 100 m, d = 19 m, t = 1/2 s
Let time taken to tavel (H – h) distance be t.
So,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE    ..(1)
Now, time taken to hit the ground is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE    ..(2)
From Eqs. (1) and (2), we get
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
⇒ a = 8 m/s2


Q.4. A particle starts from the origin at t = 0 with an initial velocity of JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE and moves in the x-y plane with a constant acceleration JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D m. The value of D is
(1) 32
(2) 50
(3) 60
(4) 40
Ans.
(3)
Solution: Given that
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
From the equation of motion in two dimensions, we have
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
⇒  t2 = 16
⇒ t = 4 s
So,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q.5. The distance x covered by a particle in one dimensional motion varies with time t as x2 = at2 + 2bt + c. If the acceleration of the particle depends on x as x−n, where n is an integer, the value of n is ______.
Ans.
3
Solution: x2 = at2 + 2bt + c
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE    .. (1)
Velocity is given by
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
⇒ vx = at + b    ..(2)
Acceleration is given by
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Differentiate Eq. (2) with respect to t, we get
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
So,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Therefore, n = 3

Q 6. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2, respectively. Then v is equal to    [JEE Main 2019]
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(2) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) 
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans: (3)
Solution: Let time taken by car A is t'
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
vB = a2(t' +t)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Put this value in Eq. (1), we get
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 7. A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of the. The ratio of times taken by the passenger train to completely cross the freight train when (i) they are moving in same direction and (ii) in the opposite directions is  [JEE Main 2019]
(1) 11/5
(2) 5/2
(3) 3/2
(4) 25/11
Ans:
(1)
Solution: 
Let passenger train and freight train be A and B and vA is the velocity of passenger train and vB is the velocity of freight train B.

Relative velocity of A with respect to B is (same direction)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Time taken by the train A to cross the train B
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Train moving in opposite direction
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Therefore, required ratio is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 8. A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5 s?    (JEE Main 2019)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(1) 10 m
(2) 6 m
(3) 3 m
(4) 9 m
Ans:
(4)
As we know that, area under v-t curve gives displacement.
therefore,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 9. A particle is moving with a velocity JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE where K is a constant. The general equation for its path is    (JEE Main 2019)
(1) y = x2 + constant
(2) y2 = x + constant
(3) y2 = x2 + constant
(4) xy = constant
Ans:
(3)
Solution: Equation for velocity of the particle is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Thus,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Now,
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Integrating both the sides, we get
y2 = x2 + constant

Q 10.  The position coordinates of a particle moving in a 3D coordinate system is given by
x = a cos ωt
y = a sin ωt
and
z = aωt
The speed of the particle is    (JEE Main 2019)
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(2) aω
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) 2aω
Ans:
(1)
Solution:
Velocity coordinates of particle is obtained by differentiating the position coordinate with respect to time, Thus:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE 
Hence, velocity of particle is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 11. In the cube of side a, as shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be    (JEE Main 2019)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(2) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans:
(3)
Solution:
Side of a cube is a
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 12. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is     (JEE Main 2019)
(1) 1 : 16
(2) 1 : 2
(3) 1 : 4
(4) 1 : 8
Ans: 
(1)
Solution:
Area covered = πR2 

A ∝ R

Thus, range
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Therefore, required ratio is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 13. Two vectors  JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE have equal magnitudes. The magnitude of 

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is n times the magnitude of JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE The angle between JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is    (JEE Main 2019)
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE 
(2) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans:
(1)
Solution:
We know that
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
According to the question
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Squaring both the sides, we get
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 14. A body is projected at t = 0 with a velocity 10 m/s at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 m/s2, the value of R is     (JEE Main 2019)
(1) 2.5 m
(2) 2.8 m
(3) 10.3 m
(4) 5.1 m
Ans:
(2)
Solution:
At t = 1:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
The radius of curvature of the trajectory is
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
= 2.77 m = 2.8 m

Q 15. A particle moves from the point JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE at t = 0 with an initial velocity JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE It is acted upon by a constant force which produces a consult acceleration JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE What is the distance of the particle from the origin at time 2s?    (JEE Main 2019)
(1) 15m
(2) 20√2m
(3) 5m
(4) 10√2m
Ans: 
(2)
Solution:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 16. All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.    (JEE Main 2018)

(1)

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(2)

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(3)

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(4)

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Ans: B
Solution:
In graph ‘2’ initial slope is zero which is not possible, since initial velocity is non-zero in all other three graphs.

Q 17. An automobile, travelling at 40 km/h, can be stopped at a distance of 40m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is (assume no skidding):    (JEE Main 2018)
(1) 75 m
(2) 160 m
(3) 150 m
(4) 100 m
Ans:
(2)
Solution:

JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE


Q 18. The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii) the time at which the car will catch up with the scooter are, respectively.     (JEE Main 2018)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(1) 337.5 m and 25 s
(2) 225.5 m and 10 s
(3) 112.5 m and 15 s
(4)  112.5 m and 22.5 s
Ans:
D
Solution:

The distance traveled in 15 seconds by both will be given by area under curve.
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Suppose after time t, they will meet, then distance traveled by both of them will be equal.
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE


Q 19. Let JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE The magnitude of a coplanar vector JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is given by:     (JEE Main 2018)
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(2) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

(4)JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans:
C
Solution:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Solving equation (i) and (ii) we get
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 20. Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?    (JEE Main 2017)
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans:
(3)
Solution:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

Q 21. A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2. The car will catch up with the bus after a time of (JEE Main 2017)
(1) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(2) 15 s
(3) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
(4) JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
Ans: 
(4)
Solution:
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE
JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE

The document JEE Main Previous year questions (2016-20): Motion Notes | Study Physics For JEE - JEE is a part of the JEE Course Physics For JEE.
All you need of JEE at this link: JEE

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