The movement of a material point is described by the equation x = 5 + 8t + 4t ^ 2. Determine the acceleration of the point.

Given:

x (t) = 5 + 8 * t + 4 * t ^ 2 – the dependence of the coordinates of a material point on time.

It is required to determine the acceleration of a material point a (m / s ^ 2).

Let’s find the dependence of the speed of a material point on time:

v (t) = x (t) ‘= (5 + 8 * t + 4 * t ^ 2)’ = 8 + 8 * t.

Let us find the dependence of the acceleration of a material point on time:

a (t) = v (t) ‘= (8 + 8 * t) = 8 m / s ^ 2.

As you can see, the acceleration of a material point is constant and equal to 8 m / s ^ 2.

Answer: the acceleration of a material point is 8 meters per second squared.