Answer to Question #333742 in Classical Mechanics for Blaze

Question

Steep safety ramps are built beside mountain highways to enable vehicles with defective brakes to stop safely. A truck enters a 250-m ramp at a high speed v0, and travels 180 m in 6 s at constant deceleration before its speed is reduced to v0/2. Assuming the same constant deceleration, determine (a) the additional time required for the truck to stop, (b) the additional distance traveled by the truck.

Answer 1

$\frac v2=v-at,$

$s=vt-\frac{at^2}2,$ $\implies$

$a=\frac{3v^2}{8s},$

$0=\frac v2-at_1,$

$t_1=\frac{4s}{3v},$

$s_1=\frac v2 t_1-\frac{at_1^2}2=\frac s3=60~m,$

$t=\frac v{2a}=\frac{4s}{3v},$

$t_1=t=6~s.$