A car travels down a lonely road at constant velocity 20.0 m/s. Suddenly, at t =

Question

A car travels down a lonely road at constant velocity 20.0  m/s. Suddenly,  at t = 0,  the driver sees a deer in the road. After a reaction time tR  = 1.5 seconds,  the driver steps on the brakes and the car then decelerates (slows down)  at constant acceleration with magnitude 4.00 m/s2 before coming to rest at time tf. Below is the velocity v vs. time t graph of the car

A car travels down a lonely road at constant velocity 20.0 m/s. Suddenly, at t = 0, the driver sees a deer in the road. After a reaction time tR = 1.5 seconds, the driver steps on the brakes and the car then decelerates (slows down) at constant acceleration with magnitude 4.00 m/s2 before coming to rest at time tf. Below is the velocity v vs. time t graph of the car's motion. What is the car's displacement (in m) at t = 1.0 seconds? What is the car's displacement (in m) at t = 4.0 seconds?

Explanation / Answer

a) for 1 sec

d =vt = 20 x 1 = 20 m

b) for 4 sec

upto 1.5 sec : d1 = 20 x 1.5   = 30 m

after that for (4 -1.5) = 2.5 sec = ut + at^2/2

d2 = 20 x 2.5 - 4x 2.5^2/2 =37.5 m

d = d1 +d2 =67.5 m

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