The equation of motion of the body x = (6 + 12t-4t ^ 2) m. What is the acceleration of the body?

Given:

x (t) = 6 + 12 * t – 4 * t² – the equation of body motion.

It is required to determine a (meter per second squared) – the acceleration of the body.

Let us find the dependence of the speed on time by fulfilling the derivative of the first degree of the equation of motion:

v (t) = x (t) ’= (6 + 12 * t – 4 * t²)’ = 12 – 8 * t.

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) = (12 – 8 * t) ’= -8 meters per second squared.

Answer: the acceleration of a body is -8 meters per second squared.