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...
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.
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Rico Grant
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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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