Question

A vehicle moving with 15 km/hr comes to rest by covering 5 m distance by applying brakes. If the same vehicle moves at 45 km/hr, then by applying brakes, it will come to rest by covering a distance of

• A. 15 m
• B. 45 m
• C. 60 m
• D. 30 m

Hint:

The stopping distance for an object is proportional to the square of its speed, so doubling the speed increases the stopping distance by a factor of four.

Answer 1

The Correct Option is B

Step 1: Using the relation for stopping distance.
The stopping distance is proportional to the square of the speed. Hence, if the stopping distance for a speed \( v_1 \) is \( d_1 \), then for a speed \( v_2 \), the stopping distance \( d_2 \) is given by: \[ \frac{d_2}{d_1} = \left( \frac{v_2}{v_1} \right)^2 \] Substituting the given values: \[ \frac{d_2}{5} = \left( \frac{45}{15} \right)^2 = 9 \Rightarrow d_2 = 45 \, \text{m} \] Step 2: Conclusion.
The correct answer is (B), 45 m.