The speed of a point moving in a straight line is given by the equation v = 3t ^ 2-2t-1.

The speed of a point moving in a straight line is given by the equation v = 3t ^ 2-2t-1. Calculate its path 5s from the beginning of the movement.

Rectilinear motion is given by the equation v = 3 * t ^ 2 – 2 * t – 1.

s (t) = v ‘(t);

We calculate the derivative of the function v = 3 * t ^ 2 – 2 * t – 1.

s (t) = v ‘(t) = (3 * t ^ 2 – 2 * t – 1)’ = (3 * t ^ 2) ‘- (2 * t)’ – 1 ‘= 3 * 2 * t – 2 * 1 – 0 = 6 * t – 2;

From here we get the equation of distance.

s (t) = 6 * t – 2;

Let’s find the path in 5 seconds from the start of the movement.

s (5) = 6 * t – 2 = 6 * 5 – 2 = 30 – 2 = 28;

Answer: s = 28.