A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and a kinetic energy K. If the same pull instead acts over twice this distance:
A) The sled's speed will be 2v and its kinetic energy will be 2K.
B) The sled's speed will be 2v and its kinetic energy will be K .
C) The sled's speed will be v and its kinetic energy will be 2K.
D) The sled's speed will be v and its kinetic energy will be K .
E) The sled's speed will be 4v and its kinetic energy will be 2K.

Question

A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and a kinetic energy K. If the same pull instead acts over twice this distance:
A) The sled's speed will be 2v and its kinetic energy will be 2K. 
B) The sled's speed will be 2v and its kinetic energy will be K . 
C) The sled's speed will be v and its kinetic energy will be 2K. 
D) The sled's speed will be v and its kinetic energy will be K . 
E) The sled's speed will be 4v and its kinetic energy will be 2K.

Quizplus · Accepted Answer

If the same pull acts over twice the distance, then the work done on the sled will be twice as much. 
Since work done = change in kinetic energy, the sled will have twice the amount of kinetic energy as before (2K).
The work-energy principle also tells us that the work done is equal to the change in kinetic energy, so:
work = (1/2)mv^2 - 0 (since it starts from rest)
If the same pull acts over twice the distance, the work done will be:
2work = (1/2)mv^2 - 0
Solving for v, we get:
v = sqrt(2work/m)
Since the mass of the sled is constant, v only depends on the work done.
Therefore, if the same pull acts over twice the distance, the sled's speed will be the same as before (v) and its kinetic energy will be twice as much (2K). 
Therefore, the answer is choice C.

A Constant Horizontal Pull Acts on a Sled on a Horizontal