The movement of a material point is described by the equation x = 20 + 2t-t²

The movement of a material point is described by the equation x = 20 + 2t-t², taking its mass equal to 4 kg. Find the impulse after 1 s and 4 s after the start of the time interval.

Given:

x (t) = 20 + 2 * t – t ^ 2 – the equation of motion of a material point;

t1 = 1 second – time interval;

t2 = 4 seconds – time interval;

m = 4 kilograms – the mass of a material point.

It is required to determine P1 and P2 (kg * m / s) – the momentum of a point at intervals t1 and t2.

Let’s find the dependence of the speed on time:

v (t) = x (t) ‘= (20 + 2 * t – t ^ 2)’ = 2 – 2 * t.

Then, the speed of the body at different intervals of time will be equal to:

v (1) = 2 – 2 * 1 = 2 – 2 = 0 m / s.

v (4) = 2 – 2 * 4 = 2 – 8 = -6 m / s.

The momentum of the point during these intervals will be equal to:

P1 = m * v1 = 4 * 0 = 0.

P2 = m * v2 = 4 * (-6) = -24 kg * m / s.

Answer: after 1 second the impulse of the point will be equal to 0, after 4 seconds the impulse of the point will be -24 kg * m / s.