The body moves with an acceleration that changes according to the law a = 10t-10. Determine the acceleration

The body moves with an acceleration that changes according to the law a = 10t-10. Determine the acceleration of the body 3 s after the start of movement and the speed at the end of the third second, if v0 = 0.

To determine acceleration, it is necessary to substitute time into the law of motion:
a = 10t-10 = 10 * 3-10 = 30-10 = 20 m / s².
The law of change in acceleration is a derivative of the law of change in speed with respect to time t.,
Let’s take an indefinite integral of acceleration:
v = ∫a (t) dt = ∫10t-10 dt = 10∫t -10∫dt = 10 * t² / 2 – 10 * t + C (for C, in this case, there should be vo = 0)
v = 10 * t² / 2 – 10 * t
Substituting time into the law of motion, we find the speed:
v = 10 * t² / 2 – 10 * t = 10 * 3² / 2-10 * 3 = 45-30 = 15 m / s.
Answer: acceleration 20 m / s, speed 15 m / s.