JEE-Main (Previous Year Questions)
1. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken
by the particle, to hit the ground, is n times that taken by it to reach the highest point of its
path. The relation between H, u and n is: [JEE(Main)-2014]
(1) 2 g H = n2u2 (2) g H = (n–2)2u2
(3) 2 g H = nu2 (n–2) (4) g H = (n–2)u2
2. A body is thrown vertically upwards. Which one of the following graphs correctly represent the
velocity vs time? [JEE(Main)-2017]
v v
(1) (2)
t
t
v v
(3) (4)
t t
3. All the graphs below are intended to represent the same motion. One of them does it
incorrectly. Pick it up. [JEE(Main)-2018]
Position Velocity Velocity distance
(1) time (2) time (3) position (4) time
1
4. A ball is dropped from the top of a 100 m high tower on a planet. In the last s before hitting
2
the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms –2) near the surface
on that planet is _____ [JEE(Main)-2020]
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 __________. [JEE(Main)-2020]
6. A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds
h
and reaches height . The velocity versus height of the ball during its motion may be
2
represented graphically by : [JEE(Main)-2020]
(1) (2) (3) (4)
Kinematics-1D and Calculus 135
, 7. A small ball of mass is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2 where v is its speed. The maximum height attained by the ball is:
[JEE(Main)-2020]
1 ku2 1 ku2 1 ku2 1 ku2
(1) tan−1 (2) ln 1 + (3) tan−1 (4) ln 1 +
2k g 2k g k 2g k 2g
8. A helicopter raises from rest on the ground vertically upwards with a constant acceleration g.
A food packet is dropped from the helicopter when it is a height h. The time taken by the packet
to reach the ground is close to [g is the acceleration due to gravity]: [JEE(Main)-2020]
2h h h 2 h
(1) t = (2) t = 1.8 (3) t = 3.4 (4) t =
3g g g 3 g
9. The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The
point S is at 4.333 seconds. The total distance covered by the body in 6s is: [JEE(Main)-2020]
49 37
(1) 12 m (2) m (3) 11 m (4) m
4 3
10. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding
acceleration-time graph? [JEE(Main)-2021]
(1) (2) (3) (4)
11. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u
and the last compartment with velocity v. The velocity with which middle point of the train
passes the signal post is: [JEE(Main)-2021]
v2 + u2 v −u u+ v v2 − u2
(1) (2) (3) (4)
2 2 2 2
12. A stone is dropped from the top of a building. When it crosses a point 5 m below the top,
another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of
building simultaneously. The height of the building is : [JEE(Main)-2021]
(1) 35 m (2) 45m (3) 50 m (4) 25m
136 Kinematics-1D and Calculus
1. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken
by the particle, to hit the ground, is n times that taken by it to reach the highest point of its
path. The relation between H, u and n is: [JEE(Main)-2014]
(1) 2 g H = n2u2 (2) g H = (n–2)2u2
(3) 2 g H = nu2 (n–2) (4) g H = (n–2)u2
2. A body is thrown vertically upwards. Which one of the following graphs correctly represent the
velocity vs time? [JEE(Main)-2017]
v v
(1) (2)
t
t
v v
(3) (4)
t t
3. All the graphs below are intended to represent the same motion. One of them does it
incorrectly. Pick it up. [JEE(Main)-2018]
Position Velocity Velocity distance
(1) time (2) time (3) position (4) time
1
4. A ball is dropped from the top of a 100 m high tower on a planet. In the last s before hitting
2
the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms –2) near the surface
on that planet is _____ [JEE(Main)-2020]
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 __________. [JEE(Main)-2020]
6. A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds
h
and reaches height . The velocity versus height of the ball during its motion may be
2
represented graphically by : [JEE(Main)-2020]
(1) (2) (3) (4)
Kinematics-1D and Calculus 135
, 7. A small ball of mass is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2 where v is its speed. The maximum height attained by the ball is:
[JEE(Main)-2020]
1 ku2 1 ku2 1 ku2 1 ku2
(1) tan−1 (2) ln 1 + (3) tan−1 (4) ln 1 +
2k g 2k g k 2g k 2g
8. A helicopter raises from rest on the ground vertically upwards with a constant acceleration g.
A food packet is dropped from the helicopter when it is a height h. The time taken by the packet
to reach the ground is close to [g is the acceleration due to gravity]: [JEE(Main)-2020]
2h h h 2 h
(1) t = (2) t = 1.8 (3) t = 3.4 (4) t =
3g g g 3 g
9. The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The
point S is at 4.333 seconds. The total distance covered by the body in 6s is: [JEE(Main)-2020]
49 37
(1) 12 m (2) m (3) 11 m (4) m
4 3
10. If the velocity-time graph has the shape AMB, what would be the shape of the corresponding
acceleration-time graph? [JEE(Main)-2021]
(1) (2) (3) (4)
11. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u
and the last compartment with velocity v. The velocity with which middle point of the train
passes the signal post is: [JEE(Main)-2021]
v2 + u2 v −u u+ v v2 − u2
(1) (2) (3) (4)
2 2 2 2
12. A stone is dropped from the top of a building. When it crosses a point 5 m below the top,
another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of
building simultaneously. The height of the building is : [JEE(Main)-2021]
(1) 35 m (2) 45m (3) 50 m (4) 25m
136 Kinematics-1D and Calculus
