Q1
The driver of a car travelling downhill on a road applies the brakes. The speed s of the car in
Kmh 1. t seconds after the brakes were applied, is given by
s(t) = -4+2+12t+80.
a. After how many seconds did it car reach its maximum speed?
b. What was the maximum speed reached?
Answers
Given : The driver of a car travelling downhill on a road applies the brakes
The speed s of the car in Km/h . t seconds after the brakes were applied, is given by
s(t) = -4t²+12t+80.
To Find : a. After how many seconds did it car reach its maximum speed?
b. What was the maximum speed reached?
Solution:
s(t) = -4t² + 12t + 80
ds/dt = -8t + 12
ds/dt = 0
=> -8t + 12 = 0
=> t = 12/8
=> t = 3/2
d²s/dt² = -8 < 0
Hence speed is maximum when t = 3/2
After 3/2 secs car reach its maximum speed
maximum speed reached = s(3/2)
= -4(3/2)² + 12(3/2) + 80
= -9 + 18 + 80
= 89
maximum speed reached = 89 km/hr
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