The point moves in a straight line according to the law s (t) = 2t ^ 3-2t ^ 2 – 4

The point moves in a straight line according to the law s (t) = 2t ^ 3-2t ^ 2 – 4 (s-in meters, t-in seconds). Find the acceleration point at the end of the second second.

Given:

S (t) = 2t ^ 3 – 2t ^ 2 – 4.

Find – a, for t = 2 s.

Solution

To find the acceleration at a given moment in time, it is necessary to write down the law of acceleration change:

a (t) = V ‘(t);

V (t) = S ‘(t);

V (t) = 3 * 2t ^ 2 – 2 * 2t;

V (t) = 6t ^ 2 – 4t;

a (t) = 2 * 6t – 4;

a (t) = 12t – 4;

a (2) = 12 * 2 – 4 = 24 – 4 = 20 (m / s ^ 2)

Answer: a = 20 m / s ^ 2.