A car is travelling along a straight, smooth road with velocity given by v(t) = 2t + t2 at time t seconds. The car drive

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A car is travelling along a straight, smooth road with velocity
given by v(t) = 2t + t2
at time t seconds. The car drives through a red traffic light at
t = 0 seconds. (i) Determine the acceleration of the car after 3
seconds.
(2 marks) (ii) Determine how far, in metres, is the car from the
traffic light after 4 seconds.
(3 marks)
(b) An object is dropped off a cliff edge which is 100m
above the sea level.
(i) Using calculus, show that the velocity of the object,
v(t), at time t is given by
v(t) = at where a is a constant to be determined. Explain your
answer carefully.
(4 marks)
(ii) Hence, or otherwise, determine the time t at which
the object is travelling at 15.7ms−1 .
(iii) Find the exact value of the time t when the object hits
the sea.