Top 10 Kinematics questions

Q1. A ball is thrown up vertically with a certain velocity so that it reaches a maximum height h. Find the ratio of the times in which it is at height h/3 while going up and coming down respectively.

• √3−1 / √3+1
• √2−1 / √2+1
• 1/3
• None of these

Q2. The displacement-time graph of a particle is shown. The average velocity during 0 to 3 s and 3 to 5 s are respectively:

• 10 m/s, 0 m/s
• 5 m/s, 2 m/s
• 6 m/s, 0 m/s
• None of these

Q3. A particle moves so that its displacement x (in m) at time t (in s) is given by x² = 1 + t². If its acceleration = x⁻ⁿ, find n.

• 2
• 3
• 4
• None of these

Q4. Two cars travel towards each other at 20 m/s each. When 300 m apart, both apply brakes with retardation 2 m/s². The distance between them when they come to rest is:

• 25 m
• 100 m
• 50 m
• None of these

Q5. The relation between time t and distance x is t = αx² + βx. The relation between acceleration (a) and velocity (v) is:

• a = −5αv⁵
• a = −2αv³
• a = −3αv²
• None of these

Q6. The velocity-time graph of an object moving along a straight line is triangular with base 4 s and height 10 m/s. The distance covered in 4 s is:

• 20 m
• 30 m
• 40 m
• None of these

Q7. A passenger in a train moving at 90 km/h observes another train moving opposite at 54 km/h for 8 s. The length of the second train is:

• 80 m
• 120 m
• 200 m
• None of these

Q8. A vehicle travels 4 km with 3 km/h and another 4 km with 5 km/h. Find the average speed.

• 3.75 km/h
• 4.25 km/h
• 3.50 km/h
• None of these

Q9. A particle moves such that its displacement x = 2t² − 3t + 1. Find instantaneous velocity at t = 2 s.

• 5 m/s
• 7 m/s
• 9 m/s
• None of these

Q10. The retardation of a body moving in a straight line is proportional to its velocity. If initial velocity is 20 m/s, find velocity after it covers 10 m.

• 14.1 m/s
• 16.5 m/s
• 12.0 m/s
• None of these

Q11. A particle is projected such that its horizontal range is three times its maximum height. The horizontal range is given as (n u² / 2.5 g). Find n.

• 6
• 12
• 18
• None of these

Q12. Two projectiles are fired from the same point at angles (45° + α) and (45° − α) with the horizontal. The ratio of their times of flights is:

• (1 + tan α) / (1 − tan α)
• (1 − sin 2α) / (1 + sin 2α)
• (1 − tan α) / (1 + tan α)
• None of these

Q13. Two balls of the same mass are projected at different angles such that the maximum height of the first is 8 times that of the second. The ratio of their total times of flight T₁ : T₂ is:

• 2 : 1
• √2 : 1
• 2√2 : 1
• None of these

Q14. The co-ordinates of a particle moving in the x–y plane are given by x = 2 + 4t and y = 3t + 8t². The motion of the particle is:

• Uniform motion along a straight line
• Non-uniformly accelerated motion
• Uniformly accelerated motion having constant acceleration
• None of these

Q15. The position of an ant moving in the Y–Z plane is S = 2t²ĵ + 5k̂ (where t is in seconds). The magnitude and direction of velocity at t = 1 s is:

• 16 m/s in y-direction
• 4 m/s in x-direction
• 9 m/s in z-direction
• None of these

Q16. The range of a projectile projected at 15° is 50 m. If projected at 45° with the same velocity, the range will be:

• 50√2 m
• 100 m
• 100√2 m
• None of these

Q17. Two projectiles are projected at 30° and 60° with equal speed. The ratio of their maximum heights is:

• 1 : √3
• √3 : 1
• 1 : 3
• None of these

Q18. A ball of 100 g is projected at 20 m/s and 60° with the horizontal. The decrease in kinetic energy when it reaches the highest point is:

• 20 J
• 15 J
• 5 J
• None of these

Q19. A stone is projected at an angle θ and returns to the same level after 4 s. If the maximum height is 20 m, find θ.

• 30°
• 45°
• 60°
• None of these

Q20. A particle is projected at velocity u making an angle θ with the horizontal. The time when its velocity makes 45° with the horizontal is:

• (u sinθ − u cosθ) / g
• (u sinθ + u cosθ) / g
• (u sinθ − √2u cosθ) / g
• None of these