A particle moving in a straight line is x cm from the point O at time t seconds (t =>0) where x= t^3 - 11t^2 +24t -3 find
For how long the particle's velocity velocity is negative
When the particle's acceleration is zero and its velocity an position at that time.
Maths
2007-11-17 3:23 am
回答 (1)
2007-11-17 3:33 am
✔ 最佳答案
x= t^3 - 11t^2 +24t -3 v = dx/dt = 3t^2-22t+24 = (3t-4)(t-6)
a=dv/dt = 6t-22
When t=4/3 and t=6,v=0;for 4/3<t<6, v<0
.'.Length of time when velocity is negative = 6 - 4/3 = 14/3 s
When a=0, t = 11/3
v(11/3) = -49/3 cm/s
x(11/3) = -367/27 cm
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