Kinetic Energy - UNSOLVED PRACTICE SET

Q7. Define kinetic energy. Write its formula and explain why it depends on the square of velocity rather than velocity itself.

Q8. State the Work-Energy Theorem. Show mathematically how it connects net work done and kinetic energy. 

Q9. A Rajdhani Express train of mass 5 × 10⁵ kg travels at 180 km/h. Calculate its kinetic energy. (First convert km/h to m/s.) 

Q10. Two stones are thrown horizontally from the same height. Stone A has mass 2 kg and speed 10 m/s. Stone B has mass 1 kg and speed 14 m/s. Which has greater kinetic energy? Show calculations.

Q11. Why is it more dangerous to be hit by a cricket ball bowled at 140 km/h than the same ball thrown at 30 km/h? Use kinetic energy to explain your answer quantitatively.

Q12. Explain how the brakes of a vehicle work from an energy perspective. What happens to the kinetic energy of the vehicle when it stops?

Q13. Derive the formula for kinetic energy (KE = ½mv²) using the concept of work done. Your derivation must include:
(a) starting with an object of mass m at rest,
(b) applying a net force F over displacement s to accelerate it to velocity v,
(c) using the equation v² = u² + 2as to express s in terms of v and a,
(d) substituting into W = Fs and simplifying to ½mv², and
(e) stating the unit and giving a real-life example.

Q14. A car of mass 800 kg is moving at 25 m/s when the driver sees a child on the road 40 m ahead and applies brakes.
(a) Calculate the initial KE of the car.
(b) Using the Work-Energy Theorem, calculate the minimum braking force needed to stop the car within 40 m.
(c) If the friction force is only 8000 N, does the car stop in time? Show calculation.
(d) What does this tell us about safe driving speeds?
(e) How does doubling the speed affect the stopping distance?

Q15. Compare the kinetic energies in the following scenarios and answer the questions:
(a) A 60 kg student runs at 5 m/s — find KE.
(b) The same student cycles at 10 m/s on a 15 kg bicycle — find total KE of student + bicycle.
(c) An 800 kg car moves at 15 m/s — find KE.
(d) Which has more KE: the running student or the cycling student?
(e) What fraction of the car's KE is the cycling student's KE?
(f) What does this comparison suggest about energy in road accidents?

Q16. A bullet of mass 0.02 kg is fired and strikes a wooden block with a velocity of 400 m/s. It embeds itself and the block (mass 2 kg) moves together.
(a) Calculate the KE of the bullet just before impact.
(b) Using conservation of momentum, find the velocity of the bullet-block system just after impact.
(c) Calculate the KE of the bullet-block system after impact.
(d) How much KE was lost? What happened to it?

Q17. A ball of mass 0.5 kg is dropped from a height of 20 m. (Use g = 10 m/s².)
(a) Calculate the velocity just before it hits the ground using v² = 2gh.
(b) Calculate the kinetic energy just before impact.
(c) If the ball bounces back to only 12 m, calculate its KE just after the bounce.
(d) How much energy was lost in the bounce?

Q18. A net force of 60 N acts on a 5 kg box initially at rest, moving it 18 m.
(a) Calculate the work done by the net force.
(b) Using the Work-Energy Theorem, find the final KE of the box.
(c) Find the final velocity of the box.
(d) If the same force now acts for an additional 10 m, find the new KE and new velocity.