The speed of movement of a material point is given by the equation V = 5 + 2t. Determine point acceleration

The speed of movement of a material point is given by the equation V = 5 + 2t. Determine point acceleration, initial speed, build a speed graph. Write the equation of motion of the point X = X (t).

Given:

v (t) = 5 + 2 * t.

It is required to determine the acceleration of the body a (m / s ^ 2), the initial velocity of the body v0 (m / s), as well as the equation of motion of the body x (t).

The velocity equation has the form:

v (t) = v0 + a * t, where v0 is the initial velocity of the body, a is the acceleration of the body.

Using the general equation of speed, we get:

v0 + a * t = 5 + 2 * t, from here we find that:

v0 = 5 m / s, a = 2 m / s ^ 2.

The general equation of body motion is:

x (t) = x0 + v0 * t + a * t ^ 2/2.

Assuming that the body began to move from the origin (x0 = 0), and substituting the known values, we get:

x (t) = 5 * t + 2 * t ^ 2/2 = 5 * t + t ^ 2.

Answer: the initial velocity of the body is 5 m / s, the acceleration of the body is 2 m / s ^ 2, the equation of motion of the body will be x (t) = 5 * t + t ^ 2.