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 4.0 kg object
B)the 1.0 kg object
C)Both objects travel the same distance.
D)It cannot be determined from the information given.

Question

Quizplus · Accepted Answer

The distance travelled by an object while braking is given by:
distance = (initial velocity)^2 / (2*braking force*mass)
Since the braking force and the mass of the two objects are the same, we can compare their distances using the formula above. We get:
For the 4.0 kg object: distance = (2.0 m/s)^2 / (2*braking force*4.0 kg)
For the 1.0 kg object: distance = (4.0 m/s)^2 / (2*braking force*1.0 kg)
If we assume that the braking force is the same for both objects, then we can see that the distances travelled will be proportional to the squares of their initial velocities. Using this, we can see that the 1.0 kg object travels four times the distance of the 4.0 kg object before stopping. Therefore, the correct answer is C: Both objects travel the same distance.

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