JEE MAIN - Physics (2023 - 12th April Morning Shift - No. 2)
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
Statement I is incorrect but Statement II is correct.
Statement $$\mathrm{I}$$ is correct but Statement II is incorrect.
Both Statement I and Statement II are correct.
Both Statement I and Statement II are incorrect.
Explanation
Statement I is correct: The kinetic energy of an object is given by $\frac{1}{2}mv^2$, where m is the mass of the object and v is its velocity. If a truck and a car are moving with the same kinetic energy and are brought to rest by applying brakes that provide equal retarding forces, both will come to rest in equal distances. This is because the distance required to stop an object depends on its initial kinetic energy and the force applied to bring it to rest. Since both the truck and car have the same initial kinetic energy and are subjected to the same retarding force, they will come to rest in the same distance.
Statement II is incorrect. When the car moves from east to north, even though its speed remains unchanged, its direction changes. Since velocity is a vector quantity that has both magnitude (speed) and direction, a change in direction implies a change in velocity. Acceleration is the rate of change of velocity, so when the velocity changes, there is acceleration. In this case, the car's acceleration is not zero as it turns from east to north.
Statement II is incorrect. When the car moves from east to north, even though its speed remains unchanged, its direction changes. Since velocity is a vector quantity that has both magnitude (speed) and direction, a change in direction implies a change in velocity. Acceleration is the rate of change of velocity, so when the velocity changes, there is acceleration. In this case, the car's acceleration is not zero as it turns from east to north.
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