- #1

Chan M

## Homework Statement

1. [/B]The only force acting on a 4.0

*kg*body as it moves along the x-axis varies as shown in the figure. The velocity of the body at x = 0 is 7.0

*m*/

*s*.

c) What is the maximum kinetic energy attained by the body between x = 0 and x = 8

*m*?

## Homework Equations

Work = delta K

K = kinetic energy

K = 0.5 * m * v^2

v = velocity

m = mass

Work is integral of the function of Force in regards to position

## The Attempt at a Solution

So in looking at the graph, 0-1 meters, K has a positive change of 2.5 J. Between 1-2 meters, K has a negative change of 2.5 J. So they cancel out, v at 0 meters equals v at 2 meters, which is 7 m/s

Also, initial kinetic energy is 98 J

98 J = 0.5 * 4kg * (7 m/s)^2

Thus, we can find the kinetic energy at 8 meters by subtracting 2 meters and starting at the 2 meter mark since K at 2 meters equals K at 0 meters because velocities are the same at these points.

And because F is constant between 2 and 8 meters, we can simply use the W = Fd equation.

So that...

F * dr = K - Ko

-5N * 6m = K - 98J

K = 68 J

I know this isn't the correct answer, I don't know why and I need to know how to get to the correct answer.

Thanks!