A car and truck are racing (dragging!) down the street. The truck is 100 feet in

Question

A car and truck are racing (dragging!) down the street. The truck is 100 feet in front of the car when a traffic light, ahead, turns red. Both begin braking at the same time and just barely stop at the light (they end up side by side in separate lanes). The truck is initially traveling at 80 ft/s. It brakes with a = -34 ft/s2 (constant). The cars acceleration (not constant) is given by a=-ao(1-(x/d) ^2 ), where d is the stopping distance for the car, and x is measured from the initial position of the car. The cars initial velocity is 100 ft/s.

How long does it take the truck to stop?

How far does the truck travel before stopping?

Explanation / Answer

for truck

vi = 80 ft/s

vf = 0 ft/s

a = -34 ft/s^2

a)
time taken for the truck to stop, t = (vf - vi)/a

= (0 - 80)/(-34)

= 2.35 s

b) distance travelled before stopping, d = (vf^2 - vi^2)/(2*a)

= (0^2 - 80^2)/(2*(-34))

= 94.1 ft

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