Who travels farther before stopping?

A 1000 kg truck and a 100 kg motorbike have the same momentum. The same constant braking force stops each of them. The ratio of their stopping distances (bike : truck) is:

Answer: 10 : 1.

The stopping distance is the kinetic energy divided by the braking force, because the work done by the brakes removes all of the kinetic energy. For a given momentum p, the kinetic energy is p²/2m.

d = \frac{K}{F} = \frac{p^{2}}{2 m F}

\Rightarrow \frac{d_{bike}}{d_{truck}} = \frac{m_{truck}}{m_{bike}} = \frac{1000}{100} = 10

So the bike travels ten times as far, even though both stop in the same time. With equal momentum the lighter vehicle carries more kinetic energy, and energy is what sets the distance.

Original practice question · JEE Physics Decoded

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