The position function of a particle in rectilinear motion is given by s(t) s(t) = t3 – 9t2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.

Question

mrnood · Answer

since there are no units in the question I don't see how you can put units in the answer...

tmagloire1 · Answer

My teacher said to ignore that part

tmagloire1 · Answer

@misty1212

irishboy123 · Answer

In order for the particle to reverse direction it must first slow to v=0. Find an equation for v(t) by differentiating s(t) and then set that to 0.

tmagloire1 · Answer

@irishboy123 
s(t) = t^3 – 9t^2 + 24t + 1 
s'(t) = 3t^2 - 18t + 24
3t^2 - 18t + 24 = 0
3t^2 - 18t = -24
t(3t-18) = -24
t= -24 and -2

tmagloire1 · Answer

@triciaal please help i really need it D:

triciaal · Answer

to check when the direction changes you need to identify turning points,
the maximum and minimums

tmagloire1 · Answer

Are -24 and -2 turning points?

triciaal · Answer

to get the acceleration take the second derivative of the original function

tmagloire1 · Answer

so acceleration is 
s'(t) = 6t - 18

tmagloire1 · Answer

s''(t)

triciaal · Answer

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