CBSE Class 11 Physics Kinematics Basic Problems

1. The displacement (x) of a particle moving in one dimension, under the action of a constant force is related to the time t by the equation t =√ x +3 where x is in metres and t is in seconds. Find the displacement of the particle when its velocity is zero.

2. A car accelerates from rest at a constant rate α for sometime after which it decelerates at a constant rate β to come to rest. If the total time lapse is t seconds, evaluate
(a) the maximum velocity reached and
(b) the total distance travelled.

3. A rocket is fired vertically from rest and ascends with constant net vertical acceleration of 30 m/sec² for 1 minute. Its fuel is then all used up and it continues as a free particle in the gravitational field of the earth. Find.
(a) maximum height reached
(b) the total time elapsed from take-off until the rocket strikes the earth.

4. A parachutist after bailing out falls 50 m, without friction. When the parachute opens, he decelerates downwards with 2.0 m/s². He reaches the ground with a speed of 3 m/sec.
(a) How long is the parachutist in the air ?
(b) At what height did he bail out ?

5. A man in a lift ascending with an acceleration f, throws a ball vertically upwards with a velocity v and catches it after time t₁. Afterwards when the lift is descending with the same acceleration, the man again throws a ball vertically upwards with the same velocity and catches it after time t₂. Determine v and f in terms of t₁, t₂ and g, the acceleration due to gravity.

6. An open elevator is ascending with constant speed v = 10 m/sec. A ball is thrown vertically up by a boy on the elevator when he is at a height of h = 30 m from the ground. The velocity of the projection is v = 20 m/sec with respect to elevator. Find

(a) the maximum height attained by the ball
(b) time taken by the ball to meet the elevator again
(c) the time taken by the ball to reach the ground after crossing the elevator.

7. A particle moves in the plane xy with constant acceleration a directed along the negative y axis. The equation of motion of the particle has the form y = αx – βx², where α and β are positive constants. Find the velocity of the particle at the origin of coordinates.

8. A particle moves along a horizontal path such that its velocity is given by v = (3t² –6t) m/s where t is he time in seconds. If it is initially located at origin O, determine the distance travelled by the particle during the time interval t = 0 to t = 3.5 seconds and the particle’s average velocity and average speed during this time period.

9. How long will a plane take to fly around a square with side a with the wind blowing at a velocity u, in the two cases:
(a) the direction of the wind coincides with one of the sides
(b) the direction of the wind coincides with one diagonal of the square? The velocity of the plane in still air v > u.

10. A stone is thrown up from the top of a tower 20 metres with a velocity of 24 metres/second at an elevation of 30º above the horizontal. Find the horizontal distance from the foot of the tower to the point at which the stone hits the ground.

11. Two bodies were thrown simultaneously from the same point : one, straight up, and the other, at angle θ = 60º to the horizontal. The initial velocity of each body is equal to v0 = 25 m/s. Neglecting the air drag, find the distance between the bodies t = 1.70 s later.

12. Two seconds after projection, a projectile is moving at 30º above the horizontal; after one more second it is moving horizontally. Find the magnitude and direction of its initial velocity. (g = 10 m/s²)

13. A ball is projected from O with an initial velocity 700 cm/s in a direction 37º above the horizontal. A ball B, 500 cm away from O on the line of the initial velocity of A, is released from rest at the instant A is projected. Find
(a) The height through which B falls, before it is hit by A.
(b) The direction of the velocity A at the time of impact
(Given g = 10 ms^–2, sin 37º = 0.6)

14. Three particles are projected simultaneously and in the same vertical plane with different velocities and at different angles. Show that the area of the triangle formed by the particles at time t is proportional to t².

15. Two bodies are projected from the same point with equal velocities in such direction that they both strike the same point on a plane whose inclination is β. If α be the angle of projection of the first, show that the ratio of their time of flight is sin (α + β): cos α.

16. Three points are located at the vertices of an equilateral triangle of side a. They all start moving simultaneously with speed v, with the first point heading continuously for the second, the second for the third, and the third for the first. How soon will the points meet.