At what point in time is the speed of the body moving along a given path s = 3t ^ 2-15t + 2 equal to 0.

At what point in time is the speed of the body moving along a given path s = 3t ^ 2-15t + 2 equal to 0. Find the acceleration of the body?

According to the condition of the problem, the length of the path that the body will pass in time t is determined by the function:

s (t) = 3 * t ^ 2 – 15 * t + 2.

Then the speed of a moving body is defined as a derivative of the path function:

v (t) = s’ (t) = 6 * t – 15.

If v (t) = 0, then

6 * t – 15 = 0,

6 * t = 15,

t = 15/6 = 5/2 = 2.5.

The acceleration of a moving body is defined as the second derivative of the path function or

derivative of the velocity function:

a (t) = s’ ‘(t) = v’ (t) = 6.