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

The work done by the constant horizontal pull is given by W=Fdcos(0)=Fd, where F is the force, d is the distance and theta is the angle between force and displacement. The work done is equal to the change in kinetic energy of the sled. So we have K=1/2mv^2=Fd.

If the same pull acts over twice the distance, the work done is 2Fd and the kinetic energy becomes 2K. 
K=Fd --> 2K=2Fd --> 2K=1/2mv^2*(2d/d) --> 2K=(1/2)mv^2*(2) --> 2K=mv^2

So the speed of the sled will be v and the kinetic energy will be 2K. Therefore, the answer is C.

A Constant Horizontal Pull Acts on a Sled on a Horizontal