A car accelerates from rest at 1.0 `m//s^2` for 20.0 seconds along a straight road . It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car.

Explanation

a) The car goes through 3 stages:
stage 1: acceleration a = 1, initial velocity = 0, t = 20 s.
Hence the distance x is given by

`x = (1/2) a t^2 = (1/2) (1) 20^2 = 200` meters
stage 2: constant speed v is the speed at the end of stage 1.

`v = a t = 1 xx 20 = 20` m/s
`x = v t = 20 `m/s` xx (1/2 hour) = 20 m/s xx 1800 s = 36,000` meters

stage 3: Deceleration to a stop, hence u = 20 `m/s` and v = 0 (stop)
`x = (1/2)(u + v) t = (1/2)(20 + 0) 30 = 300` m
Total distance `= 200 + 36,000 + 300 = 36,500` meters.