The movement of a point is described by the equation x = -2t ^ 3 + 3t ^ 2-1. what is the average

The movement of a point is described by the equation x = -2t ^ 3 + 3t ^ 2-1. what is the average speed of a point during its movement before stopping?

Given:

x = -1 + 3 * t ^ 2 – 2 * t ^ 3 – the equation of body motion.

It is required to find the average speed of the body v (m / s) during its movement until it stops.

Let us find the equation of the body’s velocity by the derivative of its coordinate function:

v (t) = x (t) ‘= (-1 + 3 * t ^ 2 – 2 * t ^ 3)’ = 6 * t – 6 * t ^ 2.

When the body stops, its speed will be zero, then:

6 * t – 6 * t ^ 2 = 0

6 * t * (1 – t) = 0

t = 1 second, that is, the body will stop 1 second after the start of movement.

Let’s find the path traversed by the body:

S = x (1) – x (0) = -1 + 3 – 2 + 1 = 1 meter.

Then the average speed will be equal to:

v = S / t = 1/1 = 1 m / s.

Answer: the average speed will be 1 m / s.