SOLUTION: The position of a particle moving along the 𝑥-axis at any time 𝑡 is given by 𝑠(𝑡)=𝑡^3−11𝑡^2+24𝑡−17. A) Find 𝑣(5) and 𝑎(5). B) Is the particle spee

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Question 1147472: The position of a particle moving along the 𝑥-axis at any time 𝑡 is given by
𝑠(𝑡)=𝑡^3−11𝑡^2+24𝑡−17.
A) Find 𝑣(5) and 𝑎(5).
B) Is the particle speeding up
or slowing down at 𝑡 = 5? Justify
Answer by ikleyn(52778) (Show Source):
You can put this solution on YOUR website!
.

(a) The velocity is the first derivative of the position function over time v(t) = = 3t^2 - 22t + 24. (1) To find v(5), substitute t= 5 into the formula (1) The acceleration is the second derivative of the position function over time a(t) = = 6t - 22. (2) To find a(5), substitute t= 5 into the formula (2). (b) At t= 5, v(5) = -11, a(5) = 8. So, the particle moves in negative direction and has positive acceleration. In the normal human language, it means that the particle DECELERATES (slowing down, moving in negative direction).