Answer
The car travels a distance of $~~122.2~feet~~$ before it comes to a stop.
Work Step by Step
We can express $50~mi/h$ in units of $ft/s$:
$(50~mi/h)\times \frac{5280~ft}{1~mi}\times \frac{1~h}{3600~s} = 73.33~ft/s$
$a(t) = \frac{dv}{dt} = a$
$v(t) = \frac{ds}{dt} = v_0+a~t$
$s(t) = s_0+v_0~t+\frac{1}{2}at^2$
We can find $t$ when $v = 0$:
$v_0+at = 0$
$at = -v_0$
$t = -\frac{v_0}{a}$
$t = -\frac{73.33}{-22}$
$t = 3.33~s$
We can let $s_0 = 0$
We can find $s$ when $t = 3.33$:
$s(t) = v_0~t+\frac{1}{2}at^2$
$s(3.33) = (73.33)(3.33)+\frac{1}{2}(-22)(3.33)^2$
$s(3.33) = 122.2$
The car travels a distance of $~~122.2~feet~~$ before it comes to a stop.
