Question

Can some solve this problem please??
A car was moving at 12.0m/s when it hit a tree according to the damage which occurred The skid marks before the crash were 10.0m long And the acceleration must have been about -7.0 m/s^2 given the nature of the marksHow fast was the car moving before the skid?

Answer 1

Let the initial speed of the car be $v_0$ and the speed before hitting the tree $v = 12 \frac{m}{s}$. Let the distance be $L = 10 m$, and the acceleration $a = -7 \frac{m}{s^2}$. The equations of the retarded motion are then:

$v = v_0 + a t$, $L = v_0 t + \frac{a t^2}{2}$.

Substituting $t = \frac{v-v_0}{a}$ from the first equation into the second, obtain:

$L = \frac{v_0(v-v_0)}{a} + \frac{a(v-v_0)^2}{2 a^2} = \frac{1}{2 a}(v^2-v_0^2)$ , from where the initial speed is $v_0 = \sqrt{v^2 - 2 S a} \approx 16.85 \frac{m}{s}$.