integration(2)
2011-02-21 3:29 am
A person drives a car along a straight road from town A to town B without stopping. After travelling for t hours from town A, the velocity of the car is (180t-90t^2) km/h.a) find the travelling timeb) find the distance between town A and town Bc) find the maximum velocity of the car
回答 (1)
2011-02-21 4:20 am
✔ 最佳答案
a) Travelling time is given by the period when v is non-zero, thus:180t - 90t2 = 0 has roots t = 0 and t = 2
Thus travelling time is 2 hours.
b) ∫ (t = 0 → 2) (180t - 90t2) dt
= [90t2 - 30t3] (t = 0 → 2)
= 120 km
c) dv/dt = 180 - 180t
d2v/dt2 = - 180
So t = 1 gives max. of v which is 90 km/h
參考: 原創答案
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