The movement of a material point is described by the equation X = 5-8t + 4t ^ 2 (m)

The movement of a material point is described by the equation X = 5-8t + 4t ^ 2 (m), taking its mass equal to 3 kg. find the momentum of the point in two seconds.

x (t) = 5 – 8 * t + 4 * t ^ 2.

m = 3 kg.

t = 2 s.

R – ?

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

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

V (t) = (5 – 8 * t + 4 * t ^ 2) “= – 8 + 4 * 2 * t.

In the expression for the speed of movement, we substitute the value t = 2 s: V (2 s) = – 8 + 4 * 2 * 2 = 8 m / s.

p = 3 kg * 8 m / s = 24 kg * m / s.

Answer: body impulse is p = 24 kg * m / s.