Answer to Question #148212 in Differential Equations for Sean

Question

A car is travelling at 100 ft/sec when the driver suddenly applies the brakes. The position
function of the skidding car is

Answer 1

After applying break, the only force acting on the skidding car is:

$$F_R=-\mu R\\$$

where R = $\mu m g$ and $\mu$ is the coefficient of friction.

Newton's equation of motion:

$$M\ddot x =-\mu R\\$$

Integrating once with initial boundary condition $\dot x(t=0)=100$ , we have

$$\dot x=100-\mu g t$$

Again integrating once with initial boundary condition $x(t=0)=0$ , we have

$$x(t)=100t- \cfrac{\mu g t^2}{2}......Eq[1]$$

The above equation represents position as a function of time.