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Length of the Time the Driver is in the Shop

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A car travelling on a straight road accelerates from rest to a speed of 15 m/s in 6 seconds. It continues at constant speed for 11 seconds and then decelerates to rest in 2 seconds. The driver gets out of the car and walks at a speed of 2 m/s for 20 seconds back to a shop which he enters. Some time later he leaves the shop and jogs to the car at a speed of 5 m/s. He arrives at the vehicle 60 seconds after it began to accelerate from rest. The diagram (attached), which has six straight line segments, shows the (t,v) graph for the motion of the driver.

(i) Calculate the initial acceleration and final deceleration of the car.
(ii) Calculate the distance the car travels.
(iii) Calculate the length of time the driver is in the shop.

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The solution calculates the length of time the driver is in the shop.

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