Equations of Motion - UNSOLVED PRACTICE SET
Chapter: Motion | Topic: Equations of Motion
EQUATIONS OF MOTION - UNSOLVED PRACTICE SET
Topic: Equations of Motion
Multiple Choice Questions
Q1. Which equation of motion is used when displacement (s) needs to be found and time (t) is known?
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- v = s/t
Q2. A body starts from rest (u = 0) and has acceleration a = 5 m/s². Its velocity after 4 seconds is:
- 0 m/s
- 20 m/s
- 5 m/s
- 4 m/s
Q3. A car decelerates from 30 m/s to 0. Using v² = u² + 2as with a = –5 m/s², the stopping distance is:
- 6 m
- 90 m
- 180 m
- 30 m
Q4. The symbol 'u' in the equations of motion stands for:
- Final velocity
- Average velocity
- Initial velocity
- Uniform velocity
Q5. Which equation does NOT contain the term 's' (displacement)?
- s = ut + ½at²
- v = u + at
- v² = u² + 2as
- s = ½(u+v)t
Q6. A stone is dropped (u = 0) from a cliff. Using g = 10 m/s², the distance it falls in 3 seconds is:
- 30 m
- 45 m
- 90 m
- 15 m
Short Answer Questions
Q7. Write all three equations of motion. For each, clearly state what every symbol stands for and the conditions under which the equations are valid.
Q8. Derive the first equation of motion (v = u + at) using the definition of acceleration. Show every step clearly.
Q9. A motorbike starts from rest and covers 200 m in 10 seconds with uniform acceleration. Calculate
(a) the acceleration, and
(b) the final velocity at the end of 10 seconds.
Q10. A train is moving at 72 km/h when the driver applies brakes. The train decelerates at 2 m/s². How far does the train travel before stopping? Which equation did you use and why?
Q11. Explain what happens to the equations of motion when u = 0 (body starts from rest). Rewrite all three equations for this special case.
Q12. A ball is thrown vertically upward at 20 m/s (take g = 10 m/s²).
(a) How long does it take to reach the maximum height?
(b) What is the maximum height reached?
Long Answer Questions
Q13. Derive the second equation of motion s = ut + ½at² graphically using the velocity–time graph of a uniformly accelerating body.
(a) Draw (or describe) the velocity–time graph clearly labelling u, v, t, and the area.
(b) Show how the area under the graph gives the displacement.
(c) Simplify the expression for the area to arrive at s = ut + ½at².
Q14. An ISRO rocket is launched from rest with uniform acceleration. It reaches a velocity of 600 m/s in just 30 seconds.
(a) Calculate the acceleration.
(b) Calculate the distance covered in 30 seconds.
(c) Calculate the velocity when it has covered 2700 m.
(d) Calculate the time taken to cover 2700 m.
(e) State which equation you used for each part.
Q15. A car driver is travelling at 90 km/h on a national highway. She sees a child on the road 100 m ahead and immediately brakes. The car decelerates at 5 m/s².
(a) Convert 90 km/h to m/s.
(b) Calculate the distance the car takes to stop.
(c) Does the car stop before reaching the child? Show full working.
(d) If the deceleration was only 3 m/s², what would happen?
(e) What is the lesson for safe driving?
Numerical / Application-Based Problems
Q16. Two motorcycles start from the same point. Bike A has initial velocity 10 m/s and acceleration 3 m/s². Bike B starts from rest with acceleration 5 m/s².
(a) Find the velocity of each bike after 6 seconds.
(b) Find the distance covered by each in 6 seconds.
(c) Which bike is ahead after 6 seconds?
Q17. A Shinkansen-style bullet train (hypothetical Indian version!) starts from rest and must reach 100 m/s before a tunnel that begins 2 km away.
(a) What minimum uniform acceleration is needed?
(b) How long will it take to reach that speed?
(c) What will its speed be after covering only 800 m?
Q18. A ball is dropped from the top of Qutub Minar (height ≈ 72 m). Take g = 10 m/s², u = 0.
(a) Find the velocity when it has fallen 45 m.
(b) Find the time taken to reach the ground.
(c) Find the velocity just before hitting the ground.
(d) What assumption are you making about air resistance?