Answer
The car was travelling at a speed of $~~80~ft/s~~$ when the brakes were first applied.
Work Step by Step
$a(t) = \frac{dv}{dt} = -16$
$v(t) = \frac{ds}{dt} = v_0-16~t$
$s(t) = s_0+v_0~t-8~t^2$
We can let $s = 0$ at $t= 0$. Then $s_0 = 0$
When $s = 200,$ then $v = 0$
We can find $t$ when $s = 200$:
$s(t) = v_0~t-8~t^2 = 200$
$(16~t)~t-8~t^2 = 200$
$8t^2 = 200$
$t^2 = 25$
$t = 5$
We can find $v_0$:
$v_0 = 16t$
$v_0 = (16)(5)$
$v_0 = 80~ft/s$
The car was travelling at a speed of $~~80~ft/s~~$ when the brakes were first applied.
