# Kinetic Energy and Work

1. A 2 kg book is at rest on a flat frictionless surface at initial position xi=0. A force F= (2.5-x2) is applied on the book. What is the Kinetic Energy of the block as it passes through x=2 m ?

2. W= Int ( force ) ; K= (1/2)mv2 ; W = K1 - K2

3. So I started out with finding the W by taking the integral of F from x=0 to x=2. Then i put the value of the work in the work-kinetic energy equation. And im stuck here cause i don't know where to use the mass of the book.

rock.freak667
Homework Helper
Well now, the value of your integral is the kinetic energy.

$$Change \ in \ kinetic \ energy = \int_{x_1} ^{x_2} F dx$$

Since it started at rest, the initial ke is 0 and the final one is 1/2mv2

so

$$\frac{1}{2}mv^2-0=\int_{x_1} ^{x_2} F dx$$