please help with d! the answer is supposed to be 120ft (says the study guide but im not sure if its a typo or not) and i keep getting 66ft. thank you!!

$A particle moves according to the law of motion $ s=f(t)=t^{3}-9 t^{2}+15 t+10, t \geq 0 $, where $ t $ is measured in se$

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please help with d! the answer is supposed to be 120ft (says the study guide but im not sure if its a typo or not) and i keep getting 66ft. thank you!!

$A particle moves according to the law of motion $ s=f(t)=t^{3}-9 t^{2}+15 t+10, t \geq 0 $, where $ t $ is measured in se$

A particle moves according to the law of motion

s = f (t) = t^{3} - 9 t^{2} + 15 t + 10, t \geq 0

, where

t

is measured in seconds and

s

is measured in feet. a. Find the velocity at time

t

. b. Find the acceleration at time

t

. c. When is the particle moving in the positive direction? d. Find the total distance traveled during the first 8 seconds and draw a diagram to illustrate the motion of the particle.

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