The body moves in a straight line according to the law S (t) = – t ^ {3} + 15t ^ {2} – 4t – 1.

The body moves in a straight line according to the law S (t) = – t ^ {3} + 15t ^ {2} – 4t – 1. Find the acceleration of the body at the moment t = 8 s.

We have the law of motion:

s (t) = -t³ + 15 * t² – 4 * t – 1.

We find the law of instantaneous speed, for this we calculate the first derivative:

v (t) = s’ (t) = -3 * t² + 30 * t – 4.

We define the law of instantaneous acceleration, for this we take the derivative with respect to instantaneous velocity:

a (t) = v ‘(t) = -6 * t + 30.

Find the acceleration at the moment t = 8 s:

a (8) = -6 * 8 + 30 = -48 + 30 = -18 units / s², i.e. the body slows down.

Answer: a (8) = -18 units / s².