Determine the impulse of a material point with a mass of 0.5 kg at time 2 s, which moves along the ОХ

Determine the impulse of a material point with a mass of 0.5 kg at time 2 s, which moves along the ОХ axis according to the law x = 2 + 3t ^ 2 + 2t ^ 3 where t is the time in seconds, x is the coordinate in meters.

m = 0.5 kg.

t = 2 s.

x = 2 + 3 * t ^ 2 + 2 * t ^ 3.

R – ?

The momentum of a body p is a vector physical quantity equal to the product of the body’s mass m by its velocity V: p = m * V.

The dependence of the body’s velocity V (t) on time is the derivative of the dependence of its coordinate on time x “(t): V (t) = x” (t).

The dependence of speed on time will look like: V (t) = (2 + 3 * t ^ 2 + 2 * t ^ 3) “= 3 * 2 * t + 2 * 3 * t ^ 2 = 6 * t + 6 * t ^ 2.

V (2 s) = 6 * 2 + 6 * (2) ^ 2 = 36 m / s.

p = 0.5 kg * 36 m / s = 18 kg * m / s.

Answer: body impulse is p = 18 kg * m / s.