# One force represented along an x-axis

## Homework Statement

The only force acting on a 2.4 kg body as it moves along the x axis varies as shown below. The velocity of the body at x = 0 is 4.0 m/s.

(a) What is the kinetic energy of the body at x = 3.0 m?

(b) At what value of x will the body have a kinetic energy of 8.0 J?

(c) What is the maximum kinetic energy attained by the body between x = 0 and x = 5.0 m?

http://www.webassign.net/hrw/hrw7_7-41.gif

## Homework Equations

Work is equal to the change in kinetic energy
W=F*d

## The Attempt at a Solution

I'm at a loss here, I really just need some help interpreting what this graph is. I think a point in the right direction might get me started so any help is appreciated. I've been struggling a bit on work and kinetic energy and were already finishing potential energy in class so any help is appreciated heh

ok i'm just stabbing in the dark here but this is what i was thinking

Ke=1/2mv^2
initial Ke + W = Ke final
so if for part a x=3 and the force is -4 at that point work should be -12.

the velocity at 0 is 4 m/s so initial kinetic energy is 19.2
19.2-12=7.2 kinetic energy at x=3

ok i figured it out on my own and for anyone else wondering out there about this problem lemme explain.

using what i said in the before post
ke=1/2mv^2
initial Ke + W = Ke final (which i'll call Kei and Kef now)
at x=3 the work area added up under the line is 2 (at 0) 0 (at 1) -2 (at 2) and -4 (at 3). Add up those areas for a total area which gives you the work of -4. Plug that W into Kei + W = Kef, and since we already know Kei from whats givin in the problem we get the answer.

part b is working backwords using the same kei + an unknown W = 8.
what you get for work is 11.2 and with 8 W at 4 and 12 W at 5 it's just a matter finding where in between you need to be.

you should be able to get C if you got this far but if not lemme know and i'll help more