Question

The driver of a car travelling downhill on a road applies the brakes. The speed s
of the car in km h-1, t seconds after the brakes were applied, is given by
s(t)=-4t2 + 12t + 80.
a How fast was the car travelling when the driver applied the brakes?
b After how many seconds was the speed of the car 88 kmh-1? Can you explain
your answer?
< After how many seconds did the car reach its maximum speed?
d What was the maximum speed reached?

Answer 1

The maximum speed reached is 89 km/h after 1.5 seconds.

Speed

Given the speed s of the car in km/h, t seconds after the brakes were applied.

s(t) = -4t² + 12t + 80

a) The brakes were applied at t = 0, hence:

• s(0) = -4(0)² + 12(0) + 80 = 80 km/h

b) At s = 88:

88 = -4t² + 12t + 80

t = 2 seconds and t = 1 second

c) The maximum speed is at s'(t) = 0

s'(t) = -8 t + 12 = 0

8t = 12

t = 1.5 seconds

s(1.5) = -4(1.5)² + 12(1.5) + 80 = 89 km/h

The maximum speed reached is 89 km/h after 1.5 seconds.

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