The movement of a material point is described by the equation x = 2-4t + 2t ^ 2. Taking its mass equal to 2 kg

The movement of a material point is described by the equation x = 2-4t + 2t ^ 2. Taking its mass equal to 2 kg, find the impulse in 2 seconds, 4 seconds after the countdown.

m = 2 kg.

t1 = 2 s.

t2 = 4 s.

p1 -?

p2 -?

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

From the dependence of the coordinates of the body on time x (t) = 2 – 4 * t + 2 * t2, it can be seen that the body moves at first equally decelerated to a complete stop, and then uniformly accelerated with acceleration a = 4 m / s2.

The initial velocity V0 = – 4 m / s shows that at first the body moves in the opposite direction of the direction of the x axis.

The dependence of the speed has the form: V (t) = V0 + a * t.

V1 = – 4 m / s + 4 m / s2 * 2 s = 4 m / s.

p1 = 2 kg * 4 m / s = 8 kg * m / s.

V2 = – 4 m / s + 4 m / s2 * 4 s = 12 m / s.

p2 = 2 kg * 12 m / s = 24 kg * m / s.

Answer: the momentum of the body will be respectively p1 = 8 kg * m / s, p2 = 24 kg * m / s.