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.
"\\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."
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