The body moves along the x-axis according to the law: x = 10 + t-3t ^ 2. What is the modulus of

The body moves along the x-axis according to the law: x = 10 + t-3t ^ 2. What is the modulus of acceleration of a moving point?

Given:

x (t) = 10 + t – 3 * t ^ 2 – the equation of motion of some material point.

It is required to determine a (meter per second squared) – point acceleration module.

Let us find the dependence of the body’s velocity on time by fulfilling the first-degree derivative of the body motion equation:

v (t) = x (t) ’= (10 + t – 3 * t ^ 2)’ = 1 – 6 * t.

Then the acceleration of the body will be equal to:

a = v (t) ’= (1 – 6 * t)’ = -6 m / s2.

Acceleration module is equal to:

| a | = | -6 | = 6 m / s2.

Answer: the modulus of acceleration of the body is 6 m / s2.