The rectilinear motion of a point is described by the law s = t ^ 6-4t ^ 4. Find its speed at time t = 2 s.

The velocity equation is equal to the derivative of the body motion equation.

s (t) = t ^ 6 – 4t ^ 4.

v (t) = s’ (t) = 6 * t ^ (6 – 1) – 4 * 4 * t ^ (4 – 1) = 6t ^ 5 – 16t ^ 3.

Let’s calculate the value of the speed at the moment of time t = 2 s.

v (t) = 6t ^ 5 – 16t ^ 3.

v (2) = 6 * 2 ^ 5 – 16 * 2 ^ 3 = 6 * 32 – 16 * 8 = 192 – 128 = 64.

Answer: the speed at time 2 s is 64.