Let s(t) = t^3 - 9t^2 + 24t be the position function of a particle moving along a coordinate line where s is in meters and t is in minutes. Find the velocity/acceleration functions and find the position, veleocity, speed and acceleration at t =1.

Expert Answers

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Given `s(t)=t^3-9t^2+24t` as the position function.

The velocity function is the derivative of the position function:

`v(t)=s'(t)=3t^2-18t+24`

The acceleration function is the derivative of the velocity function:

`a(t)=v'(t)=6t-18`

s(1)=1-9+24=16

v(1)=3-18+24=9

a(1)=6-18=-12

So at t=1:

The position is at 16m. The velocity is 9 m/min to the right . The speed is 9 m/min. The acceleration is -12 ```"m"/"min"^2` .

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