# The movement of a material point is described by the equation x = 4 + 4t-2t ^ 2. Taking its mass equal to 5 kg

**The movement of a material point is described by the equation x = 4 + 4t-2t ^ 2. Taking its mass equal to 5 kg, find the impulse 4 s after the start of the countdown, as well as the force that caused this change in impulse.**

x (t) = 4 + 4 * t – 2 * t ^ 2.

m = 5 kg.

t = 4 s.

F -?

p -?

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

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

V (4 s) = 4 + 4 * 4 = 20 m / s.

p = 5 kg * 20 m / s = 100 kg * m / s.

According to 2 Newton’s law, the force F is determined by the formula: F = m * a.

a (t) = V (t) “= x (t)” “= (4 + 4 * t)” = 4 m / s2.

F = 5 kg * 4 m / s2 = 20 N.

Answer: the momentum of the body is p = 100 kg * m / s, a force F = 20 N. acts on the body.