A 4.0-kg object is moving with speed 2.0 m/s.A 1.0-kg object is moving with speed 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 is impossible to know without knowing how long each force acts.

Question

A 4.0-kg object is moving with speed 2.0 m/s.A 1.0-kg object is moving with speed  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 is impossible to know without knowing how long each force acts.

Quizplus · Accepted Answer

Both objects experience the same braking force, which is a force that opposes their motion and slows them down. The amount of work done by this force depends on the distance traveled and the mass of the object.

The work done by the braking force can be calculated as: 
work = force x distance

The force is the same for both objects, but the distance traveled before coming to a stop is different. According to the work-energy principle, the work done by the braking force is equal to the change in kinetic energy of the object:

work = Δkinetic energy

Since both objects start with nonzero kinetic energy and end with zero kinetic energy, the work done by the braking force is the same for both objects. Therefore, the distance traveled by each object must be inversely proportional to its mass:

distance ∝ 1/mass 
distance_1/distance_2 = mass_2/mass_1 = 4/1

This means that the lighter 1.0-kg object travels four times the distance of the heavier 4.0-kg object before coming to a stop.

Therefore, the correct answer is C: Both objects travel the same distance.

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