The equation of motion for a body weighing 5 kg moves according to the law x = 4t + 4t ^ 2, determine

The equation of motion for a body weighing 5 kg moves according to the law x = 4t + 4t ^ 2, determine the momentum of the body in 4 s from the beginning of the movement.

Initial data: m (body weight) = 5 kg; the law according to which the body moves x = 4t + 4t ^ 2; t (time from the start of movement) = 4 s.

1) Let’s define the law by which the speed of the body changes: V (t) = x ‘= (4t + 4t ^ 2)’ = 4 * 1 + 4 * 2 * t = 4 + 8t.

2) Determine the speed of the body in 4 s from the beginning of the movement: V (4) = 4 + 8 * 4 = 4 + 32 = 36 m / s.

3) Calculate the impulse of the body: P = m * V = 5 * 36 = 180 kg * m / s.

Answer: The momentum of the body 4 seconds after the start of the movement will be equal to 180 kg * m / s.