Question

The stopping distance of a moving vehicle is proportional to the

• A. initial velocity
• B. cube of the initial velocity
• C. cube root of the initial velocity
• D. square of the initial velocity
• E. square root of the initial velocity

Answer 1

The Correct Option is D

The stopping distance \( d \) of a moving vehicle is related to the initial velocity \( v_0 \) by the work-energy principle. The kinetic energy of the vehicle is given by:

\[ E_k = \frac{1}{2} m v_0^2 \]

Where: - \( m \) is the mass of the vehicle, - \( v_0 \) is the initial velocity. The work done by the braking force \( F \) is equal to the kinetic energy, and the stopping distance \( d \) is related to the work done by the formula: \[ F \cdot d = \frac{1}{2} m v_0^2 \] Assuming that the braking force \( F \) is constant, we can solve for the stopping distance \( d \): \[ d \propto \frac{v_0^2}{F} \] Since the braking force is constant, we can conclude that the stopping distance is proportional to the square of the initial velocity \( v_0 \). Thus, the correct relationship is: \[ d \propto v_0^2 \] Therefore, the stopping distance is proportional to the square of the initial velocity.

Correct Answer:

Correct Answer: (D) square of the initial velocity