A particle moves along a straight line with equation of motion s(t) = t^3 ? 9t^2

Question

A particle moves along a straight line with equation of motion s(t) = t^3 ? 9t^2 + 24t
for t ? 0, where t is measured in seconds and s in feet. (show formulas and work)
(a)Find the velocity and acceleration of the particle at time t.
(b) When is the particle at rest? What is its acceleration then?
(c) When is the particle moving in the positive direction? in the negative direction?
(d) Find the total distance traveled during the first 6 seconds.

Explanation / Answer

a.)v=ds/dt=3t^2-18t+24 a=dv/dt=6t-18 b.)v=0 t^2-6t+8=0 t=2,4 s a=6(2)-18=-6 m/s^2 a=6(4)-18=6 m/s^2 c.)6t-18>0 t>3 So upto 3 s ,in -ve direction After 3 s,in +ve direction d.)s(t)=6^3-9*6^2+24*6=36 m

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