JEE Main 2023 · 12 April · morning · Single correct · +4 / −1
Given below are two statements:
Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance.
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.
In the light of given statements, choose the most appropriate answer from the options given below
- (a) Statement I is incorrect but Statement II is correct.
- (b) Statement I is correct but Statement II is incorrect.
- (c) Both Statement I and Statement II are correct.
- (d) Both Statement I and Statement II are incorrect.
Answer and solution
Answer (b) Statement I is correct but Statement II is incorrect.
Solution
Physics sir · 4 steps
Same kinetic energy and same braking force means same work needed, so same distance. Mass does not matter.
- Statement I. By the work-energy theorem, the brakes must remove all the kinetic energy K. The work done by a constant retarding force F over distance d is Fd.
F d = K ⇒ d = K/F
- Equal distances. The truck and the car have the same K and the same F, so they have the same d. Statement I is correct.
- Statement II. Acceleration is the rate of change of velocity, and velocity is a vector. Turning from east to north changes the direction of velocity even at constant speed. So the acceleration is not zero, and Statement II is incorrect.
- So. Statement I is correct and Statement II is incorrect, which is option (b).
The idea to keep. Stopping distance under a constant force is K/F, whatever the mass. Acceleration needs only a change in velocity, so a change of direction counts even when the speed stays the same.
Answer from the NTA final answer key. Solution by PrepWiser.