Answer to Question #102048 in Classical Mechanics for Sky Seo

Question

An object is moving along the plain surface by the force F = (5x)i - (3y)j.
a) How much work was done if the particle moved from (0,0) to (-6,8)?
b) What is the change in kinetic energy?
c) If the change in location occurred in 0.2 seconds, what is the average power?

Answer 1

a)

$$W=\bold{F(r_2-r_1)}$$

$$W=5\left(\frac{x^2}{2}\right)^{-6}_0-3\left(\frac{y^2}{2}\right)^{8}_0$$

$$W=5\left(\frac{6^2}{2}\right)-3\left(\frac{8^2}{2}\right)=-6\ J$$

b)

$$\Delta K=W=-6\ J$$

c)

$$P=\frac{\Delta K}{\Delta t}=\frac{-6}{0.2}=-30\ W$$