Finding total displacement for a car moving at constant acceleration A student d

Question

Finding total displacement for a car moving at constant acceleration A student drives her car at a constant acceleration along a straight test track. She first accelerates the car at 5 m/s from rest for 5 s before maintaining a constant velocity for an additional 3 s. She then applies the brakes to decelerate the car uniformly until coming to a hait within a braking distance of 105 m. The average velocity of the car over the entire test run through the total displacementms Enter your answer in figures correct to one decimal place twithout the nits.

Explanation / Answer

displacement in first 5 seconds, d1 = vo*t + (1/2)*a*t^2

= 0 + (1/2)*5*5^2

= 72.5 m

velocity after 5 seconds, v = voy + a*t

= 0 + 5*5

= 25 m/s

displacement in additional 3s, d2 = v*t

= 25*3

= 75 m

while breaking, d3 = 105 m

acceletaion of the car while breaking, a = (vf^2 - vy^2)/(2*d3)

= (0^2 - 25^2)/(2*105)

= -2.976 m/s^2

time taken to come to stop, t = (vf - vy)/a

= (0 - 25)/(-2.976)

= 8.4 s

so, average velocity = displacement/time taken

= (72.5 + 75 + 105)/(5 + 3 + 8.4)

= 15.4 m/s <<<<<<<<<-----------------------Answer

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