# Work and kinetic energy problem

1. Oct 7, 2009

### tigerlili

1. The problem statement, all variables and given/known data
A 1.8 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. The force is given by F(x) = (7.6 - x2) N, where x is in meters and the initial position of the block is x = 0. (a) What is the kinetic energy of the block as it passes through x = 4.5 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 4.5 m?

2. Relevant equations

integral from xi to xf of (7.6 - x^2) dx

k= 1/2 mv^2

3. The attempt at a solution
okay.. so, i already got part a correct by integrating the 7.6- x^2 and putting in the upper bound

what i'm confused about is part b... my TA was also confused
he said that the word 'maximum' clues us in to take the derivative... but, if you take the derivative of this, you get back to the original function

2. Oct 7, 2009

### rl.bhat

Between x = 0 to x = 4.5 m, when the F(x) is maximum, the kinetic energy will be maximum.
Find the derivative of F(x) and equate it to zero to get the position of maximum force.

3. Oct 8, 2009

### tigerlili

okay, i think i got it