Given below are two statements:
Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes 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: A truck and a car moving with same kinetic energy are brought to rest by applying brakes 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.
- Both Statement I is correct but Statement II are correct
- Both Statement I is correct but Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
The Correct Option is C
Solution and Explanation
Solution:
For a truck and a car moving with the same kinetic energy, the distance to stop under the same retarding force can be determined by using the equation:
\[
\text{Work done} = \Delta KE
\]
Since the initial kinetic energy is the same for both vehicles, the work done (force times distance) to bring them to rest will be equal. Thus, both vehicles come to rest in the same distance.
Statement II:
In Statement II, when a car changes its direction from east to north, its speed may remain constant, but its velocity is changing because velocity is a vector quantity. Since the direction of velocity is changing, the car has acceleration. Therefore, the acceleration is not zero.
\[
\Delta \vec{V} = \vec{V_f} - \vec{V_i}
\]
As velocity is changing, acceleration \( \vec{a} \neq 0 \).
Thus, Statement II is incorrect.
Thus, the correct answer is \( \boxed{1} \).
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