The movement of a material point is described by the equation x = 5-2t + t ^ 2. Taking the mass of the point

The movement of a material point is described by the equation x = 5-2t + t ^ 2. Taking the mass of the point equal to 1.5 kg, find its impulse 3 s and 5 s after the start of the movement and the change in impulse from 3 to 5 s.

x (t) = 5 – 2 * t + t ^ 2.

m = 1.5 kg.

t1 = 3 s.

t2 = 5 s.

p1 -?

p2 -?

Δp -?

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

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

V (3 s) = -2 + 6 = 4 m / s.

p1 = 1.5 kg * 4 m / s = 6 kg * m / s.

V (5 s) = – 2 + 10 = 8 m / s.

p2 = 1.5 kg * 8 m / s = 12 kg * m / s.

The change in the momentum of the body Δp is found by the formula: Δp = p2 – p1.

Δp = 12 kg * m / s – 6 kg * m / s = 6 kg * m / s.

Answer: the body impulses are p1 = 6 kg * m / s, p2 = 12 kg * m / s, the change in impulse Δp = 6 kg * m / s.