Arjuna NEET 2026 Motion in a Plane
PHYSICS
NCERT Based 5. The position of a particle is given by
1. On an open ground, a motorist follows a track that r = 3tıˆ + 2t 2 ˆj + 5kˆ , where t is in seconds and the
turns to his left by an angle of 60° after every coefficients have the proper units for r to be in
500 m. Starting from a given turn, the metres. The direction of velocity of the particle at
displacement of the motorist at the third turn is t = 1 s is
(1) 500 m (1) 53° with x-axis
(2) 500 3 m (2) 37° with x-axis
(3) 1000 m (3) 30° with y-axis
(4) 1000 3 m (4) 60° with y-axis
2. Four girls skating on circular ice ground of radius 6. In the above question, the acceleration of the
200 m start from a point P on the edge of the particle at t = 1 s is
ground and reach a point Q diametrically opposite (1) 2 ˆj ms −2 (2) −2 ˆj ms −2
to P following different paths as shown in figure. (3) 4 ˆj ms −2 (4) −4 ˆj ms −2
For which girl displacement is equal to the actual
length of path?
7. If x = 5t + 3t2 and y = 4t are the x and y co-
ordinates of a particle at any time t second where
x and y are in metre, then the acceleration of the
particle
(1) is zero throughout its motion
(2) is a constant throughout its motion
(1) A (2) B (3) depends only on its y component
(3) C (4) D (4) varies along both x and y direction
3. A particle starts moving from point (2, 10, 1). 8. A particle starts from origin at t = 0 with a
Displacement for the particle is velocity 5 𝑖̂ ms–1 and moves in
8ıˆ − 2 ˆj + kˆ . The final coordinates of the particle is
x-y plane under the action of a force which
(1) (10, 8, 2) produces a constant acceleration of 3iˆ + 2 ˆj ms–2.
(2) (8, 10, 2) The y-coordinate of the particle at the instant
(3) (2, 10, 8) when its x-coordinate is 84 m is
(4) (8, 2, 10) (1) 12 m (2) 36 m
(3) 24 m (4) 48 m
4. For any arbitrary motion in space, which of the
following relations is true? 9. In the above question, the speed of the particle at
(The average stands for average of the quantity this time is
over the time interval t1 to t2) (1) 16 ms–1 (2) 26 ms–1
–1
1 (3) 36 ms (4) 46 ms–1
(1) vaverage = v ( t1 ) + v ( t 2 )
2
r ( t 2 ) − r ( t1 ) 10. A ball is projected from the ground with a speed
(2) vaverage = 15 ms–1 at an angle with horizontal so that its
t 2 − t1
range and maximum height are equal, then ‘tan ’
(3) v (t ) = v (0) + at
will be equal to
1
(4) r (t ) = r (0) + v (0)t + at 2 (1) 1/4 (2) 1/2
2 (3) 2 (4) 4
, 11. Two guns A and B can fire bullets at speeds) 18. Two particles are projected simultaneously in the
1 km/s and 2 km/s respectively. From a point on s same vertical plane, from the same point, both
a horizontal ground, they are fired in all possible with different speeds and at different angles with
directions. The ratio of maximum areas covered horizontal. The path followed by one, as seen by
by the bullets fired by the two guns, on the ground the other, is
is (1) a vertical line
(1) 1 : 2 (2) 1 : 16 (2) a parabola
(3) 1 : 4 (4) 1 : 8 (3) a hyperbola
(4) a straight line making a constant angle
12. A water fountain on the ground sprinkles water all
(≠ 90°) with horizontal
around it. If the speed of water coming out of the
fountain is v, the total area around the fountain
19. A shell is fired from a fixed artillery gun with an
that gets wet is
initial speed u such that it hits the target on the
v2 v4 ground at a distance R from it. If t1 and t2 are the
(1) (2)
g g2 values of the time taken by it to hit the target in
v4 v2 two possible ways, the product t1t2 is
(3) (4) (1) R/g (2) R/4g
2 g2 g2
(3) R/2g (4) 2R/g
13. Two particles are projected from the same point
20. The equations of motion projectile are given by x
with the same speed u such that they have the
= 36t m and 2y = 96t – 9.8 t2 m. The angle of
same range R, but different maximum heights, h1
projection is
and h2. Which of the following is correct?
(1) R2 = 16h1h2 (2) R2 = h1h2 4 3
(1) sin − 1 (2) sin − 1
(3) R2 = 4h1h2 (4) R2 = 2h1h2 5 5
4 3
14. Which of the following is true regarding projectile (3) sin − 1 (4) sin − 1
3 4
motion?
(1) Horizontal velocity of projectile is constant.
21. The relation between the time of flight of
(2) Vertical velocity of projectile is constant
(3) Acceleration is not constant projectile Tf the time to reach the maximum height
(4) Momentum is constant tm is
(1) T f = 2t m
15. A bomb is released by a horizontal flying (2) T f = t m
aeroplane. The trajectory of the bomb is
tm
(1) a parabola (2) a straight line (3) T f =
(3) a circle (4) a hyperbola 2
(4) T f = 2 ( tm )
16. In case of a projectile motion, what is the angle
between the velocity and acceleration at the
22. A hiker stands on the edge of a cliff 490 m above
highest point?
the ground and throws a stone horizontally with a
(1) 0° (2) 45°
speed of 15 ms–1. The time taken by the stone to
(3) 90° (4) 180°
reach the ground is
(1) 5 s
17. If a body is projected with an angle to the
horizontal, then (2) 10 s
(1) its velocity is always perpendicular to its (3) 12 s
acceleration. (4) 15 s
(2) its velocity becomes zero at its maximum
height 23. In the above question, the speed with which the
(3) its velocity makes zero angle with the stone hits the ground is
horizontal at its maximum height (1) 15 ms–1
(4) The body just before hitting the ground, the (2) 90 ms–1
direction of velocity coincides with the (3) 99 ms–1
acceleration (4) 49 ms–1
PHYSICS
NCERT Based 5. The position of a particle is given by
1. On an open ground, a motorist follows a track that r = 3tıˆ + 2t 2 ˆj + 5kˆ , where t is in seconds and the
turns to his left by an angle of 60° after every coefficients have the proper units for r to be in
500 m. Starting from a given turn, the metres. The direction of velocity of the particle at
displacement of the motorist at the third turn is t = 1 s is
(1) 500 m (1) 53° with x-axis
(2) 500 3 m (2) 37° with x-axis
(3) 1000 m (3) 30° with y-axis
(4) 1000 3 m (4) 60° with y-axis
2. Four girls skating on circular ice ground of radius 6. In the above question, the acceleration of the
200 m start from a point P on the edge of the particle at t = 1 s is
ground and reach a point Q diametrically opposite (1) 2 ˆj ms −2 (2) −2 ˆj ms −2
to P following different paths as shown in figure. (3) 4 ˆj ms −2 (4) −4 ˆj ms −2
For which girl displacement is equal to the actual
length of path?
7. If x = 5t + 3t2 and y = 4t are the x and y co-
ordinates of a particle at any time t second where
x and y are in metre, then the acceleration of the
particle
(1) is zero throughout its motion
(2) is a constant throughout its motion
(1) A (2) B (3) depends only on its y component
(3) C (4) D (4) varies along both x and y direction
3. A particle starts moving from point (2, 10, 1). 8. A particle starts from origin at t = 0 with a
Displacement for the particle is velocity 5 𝑖̂ ms–1 and moves in
8ıˆ − 2 ˆj + kˆ . The final coordinates of the particle is
x-y plane under the action of a force which
(1) (10, 8, 2) produces a constant acceleration of 3iˆ + 2 ˆj ms–2.
(2) (8, 10, 2) The y-coordinate of the particle at the instant
(3) (2, 10, 8) when its x-coordinate is 84 m is
(4) (8, 2, 10) (1) 12 m (2) 36 m
(3) 24 m (4) 48 m
4. For any arbitrary motion in space, which of the
following relations is true? 9. In the above question, the speed of the particle at
(The average stands for average of the quantity this time is
over the time interval t1 to t2) (1) 16 ms–1 (2) 26 ms–1
–1
1 (3) 36 ms (4) 46 ms–1
(1) vaverage = v ( t1 ) + v ( t 2 )
2
r ( t 2 ) − r ( t1 ) 10. A ball is projected from the ground with a speed
(2) vaverage = 15 ms–1 at an angle with horizontal so that its
t 2 − t1
range and maximum height are equal, then ‘tan ’
(3) v (t ) = v (0) + at
will be equal to
1
(4) r (t ) = r (0) + v (0)t + at 2 (1) 1/4 (2) 1/2
2 (3) 2 (4) 4
, 11. Two guns A and B can fire bullets at speeds) 18. Two particles are projected simultaneously in the
1 km/s and 2 km/s respectively. From a point on s same vertical plane, from the same point, both
a horizontal ground, they are fired in all possible with different speeds and at different angles with
directions. The ratio of maximum areas covered horizontal. The path followed by one, as seen by
by the bullets fired by the two guns, on the ground the other, is
is (1) a vertical line
(1) 1 : 2 (2) 1 : 16 (2) a parabola
(3) 1 : 4 (4) 1 : 8 (3) a hyperbola
(4) a straight line making a constant angle
12. A water fountain on the ground sprinkles water all
(≠ 90°) with horizontal
around it. If the speed of water coming out of the
fountain is v, the total area around the fountain
19. A shell is fired from a fixed artillery gun with an
that gets wet is
initial speed u such that it hits the target on the
v2 v4 ground at a distance R from it. If t1 and t2 are the
(1) (2)
g g2 values of the time taken by it to hit the target in
v4 v2 two possible ways, the product t1t2 is
(3) (4) (1) R/g (2) R/4g
2 g2 g2
(3) R/2g (4) 2R/g
13. Two particles are projected from the same point
20. The equations of motion projectile are given by x
with the same speed u such that they have the
= 36t m and 2y = 96t – 9.8 t2 m. The angle of
same range R, but different maximum heights, h1
projection is
and h2. Which of the following is correct?
(1) R2 = 16h1h2 (2) R2 = h1h2 4 3
(1) sin − 1 (2) sin − 1
(3) R2 = 4h1h2 (4) R2 = 2h1h2 5 5
4 3
14. Which of the following is true regarding projectile (3) sin − 1 (4) sin − 1
3 4
motion?
(1) Horizontal velocity of projectile is constant.
21. The relation between the time of flight of
(2) Vertical velocity of projectile is constant
(3) Acceleration is not constant projectile Tf the time to reach the maximum height
(4) Momentum is constant tm is
(1) T f = 2t m
15. A bomb is released by a horizontal flying (2) T f = t m
aeroplane. The trajectory of the bomb is
tm
(1) a parabola (2) a straight line (3) T f =
(3) a circle (4) a hyperbola 2
(4) T f = 2 ( tm )
16. In case of a projectile motion, what is the angle
between the velocity and acceleration at the
22. A hiker stands on the edge of a cliff 490 m above
highest point?
the ground and throws a stone horizontally with a
(1) 0° (2) 45°
speed of 15 ms–1. The time taken by the stone to
(3) 90° (4) 180°
reach the ground is
(1) 5 s
17. If a body is projected with an angle to the
horizontal, then (2) 10 s
(1) its velocity is always perpendicular to its (3) 12 s
acceleration. (4) 15 s
(2) its velocity becomes zero at its maximum
height 23. In the above question, the speed with which the
(3) its velocity makes zero angle with the stone hits the ground is
horizontal at its maximum height (1) 15 ms–1
(4) The body just before hitting the ground, the (2) 90 ms–1
direction of velocity coincides with the (3) 99 ms–1
acceleration (4) 49 ms–1
