# Math Help - kinetic energy integral

1. ## kinetic energy integral

A 2.1 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 (x) = (4.2 - 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 = 3.3 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 3.3 m?
Thanks a ton.

2. I'm assuming that the force you posted is $(4.2 - x^2)\vec{i}$

(a) ... $\Delta KE = W = \int_0^{3.3} (4.2 - x^2)\, dx$

(b) ... $\frac{dW}{dx} = \frac{d}{dx} \int_0^x (4.2 - t^2) \, dt$

once you find it, set $\frac{dW}{dx} = 0$ and determine the x-value that minimizes W.

3. you must be a physics type, great job. But shouldn't it be the maximum W?

4. yea ... was thinking max-min and the min stuck in my head.