A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels
The greater distance before stopping?
A) the 1.0 kg object
B) the 4.0 kg object
C) Both objects travel the same distance.
D) It cannot be determined from the information given.

Question

Quizplus · Accepted Answer

Both objects travel the same distance before stopping because the work done by the braking force to stop each object is equal to the kinetic energy each had initially, which depends on $ \frac{1}{2}mv^2 $. For both objects, this value is $ \frac{1}{2}(4)(2)^2 = 8 $ J and $ \frac{1}{2}(1)(4)^2 = 8 $ J, respectively. Since the work done (force times distance) to stop each is the same and the force is constant, the distances must be equal.

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