
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 http://edugen.wiley.com/edugen/cours...ta/up/Fvec.gif(x) = (4.2  x2)http://edugen.wiley.com/edugen/cours...enta/icirc.gif 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.

I'm assuming that the force you posted is $\displaystyle (4.2  x^2)\vec{i} $
(a) ... $\displaystyle \Delta KE = W = \int_0^{3.3} (4.2  x^2)\, dx $
(b) ... $\displaystyle \frac{dW}{dx} = \frac{d}{dx} \int_0^x (4.2  t^2) \, dt$
once you find it, set $\displaystyle \frac{dW}{dx} = 0 $ and determine the xvalue that minimizes W.

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

yea ... was thinking maxmin and the min stuck in my head.