A car moves along a straight horizontal road from a point \(A\) to a point \(B\), where \(A B = 885 \mathrm {~m}\). The car accelerates from rest at \(A\) to a speed of \(15 \mathrm {~ms} ^ { - 1 }\) at a constant rate \(a \mathrm {~ms} ^ { - 2 }\). The time for which the car accelerates is \(\frac { 1 } { 3 } T\) seconds. The car maintains the speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) for \(T\) seconds. The car then decelerates at a constant rate of \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) stopping at \(B\).
Find the time for which the car decelerates.
Sketch a speed-time graph for the motion of the car.
Find the value of \(T\).
Find the value of \(a\).
Sketch an acceleration-time graph for the motion of the car.