A car, starting from rest at a point \(A\), travels along a straight horizontal road towards a point \(B\). The distance between points \(A\) and \(B\) is 1.9 km . Initially, the car accelerates uniformly for 12 seconds until it reaches a speed of \(26 \mathrm {~ms} ^ { - 1 }\). The car continues at \(26 \mathrm {~ms} ^ { - 1 }\) for 1 minute, before decelerating at a constant rate of \(0.75 \mathrm {~ms} ^ { - 2 }\) until it passes the point \(B\).
Show that the car travels 156 m while it is accelerating.
Work out the distance travelled by the car while travelling at a constant speed. [1]
Hence calculate the length of time for which the car is decelerating until it passes the point \(B\).
Sketch a displacement-time graph for the motion of the car between \(A\) and \(B\).
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