A body with a mass of m = 2 kg moves along the ОХ axis. Its coordinate changes according to the law

A body with a mass of m = 2 kg moves along the ОХ axis. Its coordinate changes according to the law x = A + Bt + Ct2, where A = 2 m, B = 3 m / s, C = 5 m / s2. What is the momentum of the body at time t = 2 s?

m = 2 kg.

x (t) = A + B * t + C * t2.

A = 2 m.

B = 3 m / s.

C = 5 m / s2.

t = 2 s.

R – ?

The momentum of the body p is determined by the product of the body mass m by the speed of its movement V: p = m * V.

When a body moves with constant acceleration, the dependence of its coordinate on time has the form: x (t) = x0 + V0 * t + a * t ^ 2/2, where x0 is the initial coordinate of the body, V0 is the initial velocity of its movement, and is the acceleration body.

From our dependence x (t) = A + B * t + C * t ^ 2, we see that x0 = A = 2 m, V0 = B = 3 m / s, a = 2 * C = 10 m / s2.

When the body moves with constant acceleration a, the speed changes according to the law: V (t) = V0 + a * t = B + 2 * C * t = 3 + 10 * t

V (2 s) = 3 m / s + 10 m / s2 * 2 s = 23 m / s.

p = 2 kg * 23 m / s = 46 kg * m / s.

Answer: body impulse is p = 2 kg * 23 m / s = 46 kg * m / s.