The equation of motion of a material point is x = 6t – t ^ 2. Find the average ground speed (in m / s) in 9 s.

Given:

x (t) = 6 * t – t ^ 2 – the equation of motion of a material point;

t = 9 seconds – time span.

It is required to determine v (m / s) – the average speed of a material point over a period of time t.

Find the initial coordinate of the body by substituting the value t = 0:

x0 = 6 * t – t ^ 2 = 6 * 0 – 02 = 0 meters.

Let’s find the coordinate of the body at time t:

x = 6 * t – t ^ 2 = 6 * 9 – 92 = 54 – 81 = -27 meters.

Then the path traversed by the point will be equal to:

S = | x – x0 | = | -27 – 0 | = | -27 | = 27 meters.

The average speed will be equal to:

v = S / t = 27/9 = 3 m / s.

Answer: the average speed of movement of a material point in 9 seconds will be equal to 3 m / s.