Question

A motorcycle and a car are moving on a horizontal road with the same velocity. What will happen if they are brought to rest by the application of brakes, which provided an equal force to retard? (Hint: A car is heavier than a motorcycle.)

• A. The motorcycle will stop at a shorter distance.
• B. The car will stop at a shorter distance.
• C. Both will stop at the same distance.
• D. Nothing can be predicted.

Answer 1

The correct option is A The motorcycle will stop at a shorter distance.

Let the mass of the car and motorcycle be M and m, respectively (M > m).
For both the vehicles,
Initial velocity = u (say)
Final velocity = 0
As per the third equation of motion, the displacement covered by the car ($s_C$) and motorcycle ($s_M$) is as follows:
$s_C$ = $\frac{v^2-u^2}{2a_C}$, $s_M$ = $\frac{v^2-u^2}{2a_M}$
According to the second law of motion, the deceleration is inversely proportional to the mass provided by the force acting on the body, and it is the same. Therefore,
$a_M$ > $a_C$
$s_M$ < $s_C$