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

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(52780) (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).

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