A car driver makes a journey in a straight line from A to B, starting from rest. The speed of the car increases to a maximum, then decreases until the car is at rest at B. The distance travelled by...

A car driver makes a journey in a straight line from A to B, starting from rest. The speed of the car increases to

a maximum, then decreases until the car is at rest at B. The distance travelled by the car t seconds after leaving

A is 0.0000117(400t³ − 3t⁴) metres.
(i) Find the distance AB.
(ii) Find the maximum speed of the car.

(iii) Find the acceleration of the car
(a) as it starts from A,
(b) as it arrives at B.
(iv) Sketch the velocity-time graph for the journey.