A truck is traveling at a constant velocity of 20m s^-1 (72 km.h^-1) when the driver sees a child 50 m in front of him, on the road. He hits the brake to stop the truck, which accelerates at a rate of -1.25 m.s^-2. His reaction time to hit the brake is 0.5 s. Will the truck hit the child?
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Expert Answers
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Speed of the truck = 20 m/s
distance to the child = 50 m
Acceleration = -1.25 m/s^2
Reaction time = 0.5 s
During the 0.5 seconds, that the driver takes to hit the brakes, the truck will travel 10 m ( = 20 m/s x 0.5 sec).
Using the equation of motion, relating initial and final velocity, acceleration and distance traveled: v^2 = u^2 + 2as
we can calculate the distance traveled by assuming final velocity to be zero.
thus, s = (v^2 - u^2)/2a = -(20x20)/(2x-1.25) = 160 m.
Thus, the truck will travel a total distance of 170 m (= 10 m + 160 m) before it stops. Since the child is only 50 m in front of the truck, the truck will (unfortunately) hit the child, before it stops.
Hope this helps.