Kinematics: The Ultimate 50-Question Challenge

 

For NEET, JEE Mains & JEE Advanced Aspirants

Welcome to **Physics Power House**! Today, we're pushing your understanding of Kinematics to the absolute limit. This carefully curated set of 50 multiple-choice questions spans three difficulty levels, ensuring comprehensive preparation for India's toughest entrance examinations.

Question Distribution

Level	Target Exam	Questions	Focus Areas
Level 1: Foundation	NEET, JEE Mains	Q1-15	Core concepts, basic equations, graph interpretation
Level 2: Advanced Application	JEE Mains, JEE Advanced	Q16-35	Multi-concept problems, relative motion, projectile motion
Level 3: Expert Challenge	JEE Advanced	Q36-50	Non-inertial frames, variable acceleration, complex constraints

 

LEVEL 1: Foundation

Building Your Kinematics Core

Q1. A car accelerates from rest at a constant rate of 2 m/s². What distance does it cover in the 4th second of its motion?

A) 7 m 

B) 9 m 

C) 14 m 

D) 16 m  

Ans. A 

Q2. The displacement-time graph of a moving particle is a straight line inclined at 30° to the time axis. What is its velocity?

A) 0.5 m/s 

B) 0.577 m/s 

C) 1 m/s 

D) 1.732 m/s  

Ans. B 

 

Q3. A ball is thrown vertically upward with velocity 20 m/s. The distance covered by the ball in the last second of its upward journey is (g = 10 m/s²):

 A) 5 m 

B) 10 m 

C) 15 m 

D) 20 m  

Ans. A

 

Q4. Which of the following statements is INCORRECT about a freely falling body?

A) It has uniform acceleration 

B) Its velocity-time graph is a straight line 

C) Its displacement-time graph is parabolic 

D) Its speed remains constant  

Ans. D 

 

Q5. The area under acceleration-time graph gives:

A) Velocity 

B) Displacement 

C) Change in velocity 

D) Distance  

 Ans. C

 

Q6. A particle moves along a straight line such that its displacement x = t³ - 6t² + 9t + 4. The particle comes to rest at:

A) t = 1 s only 

B) t = 2 s only 

C) t = 1 s and t = 3 s 

D) t = 2 s and t = 4 s  

Ans. C

 

Q7. If a body covers equal distances in equal intervals of time, its motion is:

A) Uniform 

B) Non-uniform 

C) Accelerated 

D) Circular  

Ans. A

 

Q8. A train 100 m long moving at 36 km/h crosses a bridge in 20 seconds. The length of the bridge is:

A) 100 m 

B) 200 m 

C) 300 m 

D) 400 m  

Ans. A

 

Q9. The velocity of a particle is given by v = 3t² - 2t + 5. Its acceleration at t = 2 s is:

A) 8 m/s² 

B) 10 m/s² 

C) 12 m/s² 

D) 14 m/s²  

Ans. B

Q10. For a particle moving with constant acceleration, which graph is a straight line?

A) v-t graph 

B) s-t graph 

C) s-v graph 

D) a-t graph  

Ans. A 

 

Q11.A stone is dropped from a cliff and its splash is heard after 4 seconds. If velocity of sound is 320 m/s, the height of the cliff is approximately (g = 10 m/s²):

A) 40 m 

B) 60 m 

C) 72 m 

D) 80 m  

Ans. C 

 

Q12. A particle starting from rest moves with constant acceleration. The ratio of distances covered in the 1st, 2nd, and 3rd seconds is:

A) 1:2:3 

B) 1:3:5 

C) 1:4:9 

D) 1:1:1  

Ans. B

 

Q13. A body is projected vertically upward with velocity u. The time after which it returns to the point of projection is:

A) u/g 

B) 2u/g 

C) u/2g 

D) 2g/u  

Ans. B

 

Q14. The slope of velocity-time graph gives:

A) Distance 

B) Displacement 

C) Acceleration 

D) Speed  

Ans. C 

 

Q15. Two balls are thrown simultaneously: one vertically upward with speed u, the other vertically downward with same speed u from the same height. The time difference in reaching the ground will be:

A) u/g 

B) 2u/g 

C) 4u/g 

D) Zero 

 Ans. B

 

LEVEL 2: Advanced Application

Building Analytical Depth

Q16. A projectile is thrown with velocity 20√2 m/s at 45° to horizontal. Its radius of curvature at the point of projection is:

A) 40√2 m 

B) 80 m 

C) 40 m 

D) 20√2 m  

Ans. A

 Q17. A particle is projected from ground at angle θ with horizontal with speed u. The average velocity of the particle between point of projection and highest point is:

A) u cos θ 

B) (u/2) √ (1 + 3 cos² θ) 

C) (u/2) √ (1 + cos² θ) 

D) (u/√2)  

Ans. B

 

Q18. A swimmer can swim at 4 m/s in still water. He wants to cross a river flowing at 3 m/s. Minimum time taken to cross is 20 seconds. Width of river is:

A) 60 m 

B) 80 m 

C) 100 m 

D) 120 m  

Ans. B 

 

Q19. Rain is falling vertically at 10 m/s. A person runs at 10 m/s on horizontal ground. The angle at which he should hold umbrella to protect himself is:

A) 30° with vertical 

B) 45° with vertical 

C) 60° with vertical 

D) 90° with vertical  

Ans. B 

 

Q20. Two particles are projected simultaneously from same point with same speed but at different angles. Their horizontal ranges are equal. If one is projected at 30°, the other is projected at:

A) 45° 

B) 60° 

C) 75° 

D) 90°  

Ans. B

 

Q21.A particle moves along a circle of radius R with speed v = kt. Its total acceleration at time t is:

A) k 

B) k²t²/R 

C) √ (k² + k⁴t⁴/R²) 

D) √ (k²t² + k⁴t⁴/R²)  

Ans. C 

 

Q22. The position vector of a particle is r = (3t) î + (4t - 5t²) ĵ. The time when velocity vector becomes perpendicular to acceleration vector is:

A) 0.2 s 

B) 0.3 s 

C) 0.4 s 

D) 0.5 s  

Ans. C

 

Q23. A particle is projected from ground at 60° with horizontal. After 2 seconds, its velocity makes 30° with horizontal. Initial speed of projection is (g = 10 m/s²):

A) 10√3 m/s 

B) 20√3 m/s 

C) 30 m/s 

D) 40 m/s  

Ans. B

 

Q24. A boat crosses a river of width 500 m. The river flows at 3 m/s and boat speed in still water is 5 m/s. The drift of boat when it crosses in minimum time is:

A) 100 m 

B) 200 m 

C) 300 m 

D) 400 m  

Ans. C

 

Q25.A particle is projected from ground with speed u at angle θ. Its speed at half the maximum height is:

A) u cos θ 

B) √ (u² cos² θ + u² sin² θ/4) 

C) √ (u² cos² θ + u² sin² θ/2) 

D) u/√2  

Ans. C

 

Q26. A man can throw a ball to maximum horizontal distance of 80 m. The maximum height he can throw in same throw is:

A) 20 m 

B) 40 m 

C) 60 m 

D) 80 m  

Ans. A

 Q27. Two trains A and B of length 200 m each are moving on parallel tracks. Train A with 72 km/h and Train B with 54 km/h in same direction. The time taken by train A to overtake train B completely is:

A) 40 s 

B) 60 s 

C) 80 s 

D) 100 s  

Ans. C

 

Q28. A particle moves along x-axis such that its acceleration a = -4x, where x is position. If at t = 0, particle is at x = 0 with velocity 4 m/s, its velocity at x = 2 m is:

A) 0 

B) 2 m/s 

C) 4 m/s 

D) 8 m/s  

Ans. A

 

Q29. A stone is dropped from a balloon rising at 10 m/s when balloon is at height 100 m. The time taken by stone to reach ground is (g = 10 m/s²):

 A) 4 s 

B) 5 s 

C) 6 s 

D) 7 s  

Ans.C

 

 Q30. A car moves with velocity v₁ for half time and v₂ for remaining half time. Average velocity is:

A) (v₁ + v₂)/2 

B) 2v₁v₂/ (v₁ + v₂) 

C) √(v₁v₂) 

D) (v₁² + v₂²)/ (v₁ + v₂)  

Ans. A

 

Q31. A particle is projected at 60° with horizontal. The ratio of kinetic energy at point of projection to kinetic energy at highest point is:

A) 1:4 

B) 4:1 

C) 2:1 

D) 1:2  

Ans. B

 

Q32. A ball is dropped from height h onto a horizontal surface. If coefficient of restitution is e, the total distance covered before coming to rest is:

A) h 

B) h (1 + e²)/ (1 - e²) 

C) h (1 - e²)/ (1 + e²) 

D) 2h  

Ans. B

 

Q33. Two bullets are fired simultaneously: one horizontally from height h and other from ground with velocity making angle θ to hit the first. They collide in mid-air. The value of tan θ is:

A) √(h/g) 

B) √(2h/g) 

C) √(g/2h) 

D) √(g/h)  

Ans. B

 

Q34. A particle moves in x-y plane with velocity v = 2î + 4tĵ. Its acceleration at t = 1 s is:

A) 2 m/s² 

B) 4 m/s² 

C) 6 m/s² 

D) 8 m/s²  

Ans. B 

 

Q35. A boat crosses a river of width d flowing at velocity v. Boat speed relative to water is u > v. The angle at which boat should be directed to reach directly opposite point is:

A) sin⁻¹(v/u) 

B) cos⁻¹(v/u) 

C) tan⁻¹(v/u) 

D) cot⁻¹(v/u)  

Ans. A

 

LEVEL 3: Expert Challenge

Pushing the Boundaries

Q36. A particle moves along x-axis with acceleration a = -kx, where k is constant. If at t = 0, x = 0 and v = v₀, the maximum displacement of particle is:

A) v₀/k 

B) v₀√k 

C) v₀/√k 

D) v₀²/k  

Ans. C

 

Q37. A particle is projected from ground with speed u at angle θ. Another particle is simultaneously projected from top of tower of height h with same speed and angle to hit the first. The value of h for collision is:

A) (u² sin² θ)/g 

B) (u² sin θ cos θ)/g 

C) (u² sin 2θ)/2g 

D) (u² cos² θ)/2g  

Ans. A 

 

Q38. In the following dependent motion system, if block A moves down with velocity 2 m/s, velocity of block B is:

[Image: Complex pulley system with multiple constraints]

A) 0.5 m/s up 

B) 2 m/s up 

C) 4 m/s up 

D) 8 m/s up  

Ans. A

 

Q39. A particle is projected from ground at angle θ with horizontal on an inclined plane of inclination α (α < θ). The time of flight on inclined plane is:

A) (2u sin θ)/ (g cos α) 

B) (2u sin (θ - α))/ (g cos α) 

C) (2u sin θ)/ (g cos (θ - α)) 

D) (2u sin (θ - α))/(g)  

Ans. B

 

 Q40. A particle moves along a curve with position r = (a cos ωt) î + (a sin ωt) ĵ + (bt)k̂. Its speed at time t is:

A) aω 

B) √ (a²ω² + b²) 

C) √ (a²ω² sin² ωt + a²ω² cos² ωt + b²) 

D) aω + b  

Ans. B

 

Q41. A car starts from rest with constant acceleration a. At the same instant, a truck moving with constant speed v overtakes the car. The time after which they meet again is:

A) v/a 

B) 2v/a 

C) 3v/a 

D) 4v/a  

Ans. B

 

Q42. A particle is projected up an inclined plane of inclination β with speed u at angle α with horizontal (α > β). The range on inclined plane is maximum when α is:

A) 45° 

B) 45° + β/2 

C) 45° - β/2 

D) 90° - β  

Ans. B

 

Q43.The velocity-time graph of a particle moving along x-axis is shown. The total distance covered in first 10 seconds is:

[Image: Complex v-t graph with multiple slopes]

A) 0 m 

B) 25 m 

C) 50 m 

D) 75 m  

Ans. C

 

Q44. Two particles are projected simultaneously from same point with same speed u at angles θ and (90° - θ). The time after which their velocities become parallel is:

A) u/g 

B) u/ (g cos θ) 

C) u/ (g sin θ) 

D) 2u/g  

Ans. B

 

Q45. A particle moves along x-axis with velocity v = √ (a² - x²). Its acceleration is:

A) Zero 

B) Constant 

C) -x 

D) -v  

Ans.C

 

Q46. A man wants to cross a river of width 500 m. River flows at 4 m/s. Man can swim at 3 m/s. The minimum distance covered by man to cross the river is:

A) 500 m 

B) 625 m 

C) 750 m 

D) 1000 m  

Ans.B

 

Q47. A particle is projected from ground with speed u at angle θ. Another particle is dropped from height h at the same instant. For them to collide in mid-air, h should be:

A) (u² sin² θ)/2g 

B) (u² sin² θ)/g 

C) (2u² sin² θ)/g 

D) (u² sin 2θ)/g  

Ans.  B

 Q48. The acceleration of a particle is given by a = -ω²x. If at t = 0, x = A and v = 0, the time when kinetic energy equals potential energy is:

A) π/(4ω) 

B) π/(2ω) 

C) π/ω 

D) 2π/ω  

Ans. A

 

Q49. In a pulley system with multiple constraints, if block A moves down with acceleration 2 m/s², the acceleration of block B is:

[Image: Complex constraint motion with 3 blocks]

A) 1 m/s² up 

B) 2 m/s² up 

C) 4 m/s² up 

D) 8 m/s² up 

 Ans. A

 

Q50. A particle is projected from ground on an inclined plane of inclination 30°. The angle of projection with horizontal for maximum range on inclined plane is:

A) 45° 

B) 60° 

C) 75° 

D) 90°  

Ans. B

 

 

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