The dependence of the speed of movement of a material point on time has the form v = 4t (m / s).

The dependence of the speed of movement of a material point on time has the form v = 4t (m / s). Find the path (m) covered in the fifth second of the movement.

V = 4 * t.

t1 = 4 s.

t2 = 5 s.

S -?

From the dependence of the speed on time V = 4 * t we see that the body moves uniformly accelerated from a state of rest V0 = 0 m / s and acceleration a = 4 m / s2.

With uniformly accelerated motion, the coordinate of the body x changes according to the law: x (t) = x0 + V0 * t + a * t ^ 2/2.

The path S traversed by the body is expressed by the formula: S = x2 – x1 = x0 + V0 * t2 + a * t2 ^ 2/2 – x0 – V0 * t1 – a * t1 ^ 2/2 = a * (t2 ^ 2 – t1 ^ 2) / 2.

S = 4 m / s2 * ((5 s) ^ 2 – (4 s) ^ 2) / 2 = 18 m.

Answer: in the fifth second of movement, the body will cover the path S = 18 m.