Question

A child applies a force F parallel to the z-axis to a 6.00 kg sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the 2-component of the force she applies varies with the 2-coordinate of the sled as shown in figure (Figure 1). Suppose the sled is initially at rest at x = 0. You can ignore friction between the sled and the surface of the pond. 

For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Motion on a curved path.

Part A 

Use the work-energy theorem to find the speed of the sled at 8.0 m. 

Part B 

Use the work-energy theorem to find the speed of the sled at 12.0 m. 

Answer 1

a)

Workdone = area under F-x curve

here workdone staored as kE in object

0.5 m v^2 = area of triangle having base ( 8m). amd height ( 10N)

0.5* 6* v^2 = 0.5* 8* 10

v = 3.651 m/s

====

b)

similarly

0.5 m v^2 = area of triangle (base = 12 m, height = 10 N)

0.5* 6 v^2 = 0.5* 12* 10

v = 4.472 m/s

======

Comment before rate in case any doubt, will reply for sure.. goodluck