Question

use the work - energy theorem to find the distance over which the force acts. express your answer in terms of the variables m, v, and f. d =

Explanation:

Step1: Recall work - energy theorem

The work - energy theorem states that the net work done on an object is equal to its change in kinetic energy. The work done by a force $F$ over a distance $d$ is $W = Fd$, and the change in kinetic energy of an object of mass $m$ with an initial velocity of 0 and a final velocity $v$ is $\Delta K=K_f - K_i=\frac{1}{2}mv^{2}-0$.

Step2: Set work equal to change in kinetic energy

Since $W=\Delta K$, we have $Fd=\frac{1}{2}mv^{2}$.

Step3: Solve for $d$

Dividing both sides of the equation $Fd=\frac{1}{2}mv^{2}$ by $F$ gives $d = \frac{mv^{2}}{2F}$.

Answer:

$d=\frac{mv^{2}}{2F}$