# The equation of motion of the body: x = 5 + 3t-2t2. Describe the nature of the body movement.

**The equation of motion of the body: x = 5 + 3t-2t2. Describe the nature of the body movement. What is its speed and acceleration, explain where you got it from. Record the speed versus time.**

Given:

x = 5 + 3 * t – 2 * t ^ 2 – the equation of body motion.

It is required to define:

v0 (m / s) is the initial velocity of the body;

a (m / s2) – body acceleration;

describe the nature of the body’s motion and find the dependence of the speed on time.

To determine the dependence of speed on time, it is necessary to perform the first-degree derivative of the equation of motion:

v (t) = (5 + 3 * t – 2 * t ^ 2) ‘= 3 – 4 * t.

Substituting in the dependence of the speed on time t = 0 (the initial moment of time), we determine the initial speed:

v0 = 3 – 4 * 0 = 3 – 0 = 3 m / s.

Let us find the acceleration of the body by performing the first-degree derivative of the dependence of the speed on time:

a = v (t) ‘= (3 – 4 * t) = -4 m / s2.

Since the acceleration is negative, the body is moving equally slowly.

Answer: the speed is 3 m / s, the acceleration is -4 m / s2, v (t) = 3 -4 * t, the body is moving equally slowly.