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Starting from rest, a car speeds up uniformly to 9.80 m/s in a time of 12.0...

Starting from rest, a car speeds up uniformly to 9.80 m/s in a time of 12.0 s. The car then travels with this speed for 20 seconds before slowing down at a constant rate to a stop in 24.0 seconds. Determine the total distance in meters traveled from start to end. Round your final answer to three significant figures.

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Answer #1

Acceleration of the car

a = v/t = 9.8 / 12 = 0.8167 m/s^2

Distance travelled in 12 s

d1 = 0.5 at^2 = 0.5* 0.8167* 12^2 = 58.8 m

Distance travelled in uniform velocity

d2 = 20 * 9.8 = 196 m

Deceleration in next 24 s

a' = 9.8 / 24 = 0.40833 m/s^2

Displacement travelled

d3 = 9.8^2 / ( 2* 0.40833) = 117.6 m

Total distance

D = d1 + d2 + d3 = 58.8 + 196 + 117.6 = 372.4 m

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