Question

A loaded bus and an unloaded bus are both moving with the same kinetic energy. The mass of the former is twice that of the later. Brakes are applied to both so as to exert equal retarding forces. If $S_1$ and $S_2$ are the distances covered by the two buses before coming to rest respectively, then:

• A. $4S_1 = S_2$
• B. $2S_1 = S_2$
• C. $S_1 = 2S_2$
• D. $S_1 = S_2$

Hint:

Stopping distance depends solely on the ratio of kinetic energy to retarding force ($\frac{K}{F}$).
Since mass does not explicitly appear in this work-energy relation when kinetic energy is kept constant, mass differences do not affect the stopping distance.

Answer 1

The Correct Option is D

Step 1: Express stopping distance from kinematics instead of pure energy bookkeeping.
Using $v^2 = u^2 - 2aS$ with the bus coming to rest, $S = \frac{v^2}{2a}$, where $a$ is the deceleration produced by the retarding force.
Step 2: Bring in mass and kinetic energy separately.
Since $v^2 = \frac{2K}{m}$ (from $K=\frac{1}{2}mv^2$) and $a=\frac{F}{m}$ (from Newton's second law), substituting both into the distance formula gives \[ S = \frac{2K/m}{2F/m} = \frac{K}{F} \]
Step 3: Notice the mass cancels.
The mass $m$ drops out entirely, so $S$ depends only on the (equal) kinetic energy $K$ and the (equal) retarding force $F$ for both buses.
\[ \boxed{S_1 = S_2} \]