A material point moves along a straight line according to the law x = A + B * t ^ 4, where A = 1 m

A material point moves along a straight line according to the law x = A + B * t ^ 4, where A = 1 m, B = 2 m / s ^ 4. Find the speed of the point at time t = 2 s. Is this movement uniform or uniformly accelerated, and why?

We have the law of displacement from time to time:

x (t) = 1 + 2 * t4.

Let’s calculate the law of speed variation in time, for this we will find the derivative:

x ‘(t) = v (t) = 8 * t³.

The speed at the moment t = 2 s is equal to:

v (2) = 8 * 2³ = 8 * 8 = 64 m / s.

Let’s find the law of acceleration change:

a (t) = x ” (t) = v ‘(t) = 24 * t².

We see that the acceleration is not constant in time, i.e. the movement is neither uniformly accelerated, nor even more uniform. This is a more complex type of movement.

The rate of change of acceleration over time:

a ‘(t) = 48 * t.