Newton's Second Law of Motion - UNSOLVED PRACTICE SET

Q7. State Newton's Second Law of Motion. Write the mathematical form and define each symbol used.

Q8. Define momentum. Write its formula and state whether it is a scalar or vector quantity. Give one example showing how momentum depends on both mass and velocity.

Q9. A cricketer moves his hands backward while catching a fast ball. Explain this action using Newton's Second Law. What would happen if he kept his hands stiff?

Q10. A fully loaded school bus and an empty one have the same engine force applied. Which accelerates more? Explain using Newton's Second Law.

Q11. Show that Newton's First Law is a special case of Newton's Second Law. What condition (value of F) gives us the First Law result?

Q12. Explain why a karate expert can break a wooden plank with a bare hand. Use the concept of rate of change of momentum in your answer.

Q13. Derive Newton's Second Law using the concept of momentum. Your derivation must include:
(a) definition of momentum p = mv,
(b) expression for rate of change of momentum,
(c) statement of proportionality F ∝ Δp/Δt,
(d) introduction of proportionality constant to get F = ma,
(e) definition of 1 Newton from the equation.

Q14. An auto-rickshaw driver in Pune applies brakes and stops from 54 km/h in 6 seconds. The total mass of auto + passengers = 480 kg.
(a) Convert 54 km/h to m/s.
(b) Find the deceleration.
(c) Calculate the braking force.
(d) Calculate the initial momentum.
(e) Verify Newton's Second Law by checking if F = Δp/Δt.

Q15. Using the context of a shot-put event at a school sports day:
(a) When the athlete pushes the shot-put with greater force, what happens to its acceleration?
(b) A 4 kg shot-put vs a 7 kg shot-put — same push force — which goes farther and why?
(c) Calculate the acceleration for each shot-put if the applied force is 280 N.
(d) If the 4 kg shot-put reaches 14 m/s from rest in 0.5 s, verify the force using F = ma and also using F = Δp/Δt.

Q16. A bullet of mass 20 g is fired from rest and leaves the barrel at 350 m/s. The barrel is 70 cm long.
(a) Convert units to SI. 

(b) Calculate the acceleration using v² = u² + 2as.
(c) Calculate the force on the bullet using F = ma.

Q17. A 10 kg box is pushed along a rough floor. Applied force = 75 N, friction = 25 N.
(a) Calculate net force.
(b) Calculate acceleration.
(c) Find velocity after 5 s starting from rest.
(d) Find distance covered in 5 s.

Q18. A Vande Bharat Express (mass = 4.5 × 10⁵ kg) accelerates from rest to 30 m/s in 2 minutes.
(a) Calculate acceleration.
(b) Calculate net force needed.
(c) If total resistance = 4 × 10⁴ N, find the engine thrust.
(d) What is the train's momentum at 30 m/s?