The material point moves according to the law x = 0.5t ^ 2. What kind of movement is this?

The material point moves according to the law x = 0.5t ^ 2. What kind of movement is this? What is the point acceleration?

The movement x = 0.5t² of a material point corresponds to uniformly accelerated motion, which is given by the formula: S = V0 * t + a * t² / 2, since the first term in the law of motion is absent, the point moves uniformly accelerated without initial speed (initial speed is zero) …
The point acceleration is determined by taking the double derivative (second-order derivative):
x ‘= V = (0.5t²)’ = 2 * 0.5 * t = t.
x ” = V ‘= a = t’ = 1 m / s².
Answer: The movement is uniformly accelerated, the acceleration of the point is 1 m / s².