7. A car starts from rest at time \(t = 0\) and moves along a straight road with constant acceleration 4 \(\mathrm { ms } ^ { - 2 }\) for 10 seconds. It then travels at a constant speed for 50 seconds before decelerating to rest over a further distance of 240 m .

1. Sketch a graph of velocity against time for the total period of the car's motion.
2. Find the car's average speed for the whole journey. In reality the car's acceleration \(a \mathrm {~ms} ^ { - 2 }\) in the first 10 seconds is not constant, but increases from 0 to \(4 \mathrm {~ms} ^ { - 2 }\) in the first 5 seconds and then decreases to 0 again. A refined model designed to take account of this uses the formula \(a = k \left( m t - t ^ { 2 } \right)\) for \(0 \leq t \leq 10\).
3. Calculate the values of the constants \(k\) and \(m\).
4. Find the acceleration of the car when \(t = 2\) according to this model.