Question

Скорость материальной точки массой 1 кг при прямолинейном движении изменяется по закону хx = 5 + 0,5t ( м/ с). Через сколько секунд импульс точки изменится на 4 кг · м/ с?

Answer 1

x= 5 +0.5t
отсюда мы узнаем что начальная скорсть равна 5 и ускорение сонаправлена с вектором скорости и равно 0.5
начаьный импульс равне mv=5 конечный равен 9 поскольку масса не меняется а меняется лиш скорость то при импульсе 9 скорость равна 9
время находим по фрмуле 9=5+0.5t  t=8

Answer 2

Calculation of Impulse Change

To determine the time it takes for the impulse of a point with a mass of 1 kg to change by 4 kg·m/s, we need to analyze the given information.

The equation for the velocity of the point is given as x(t) = 5 + 0.5t (m/s)

Impulse is defined as the change in momentum of an object and is calculated as the product of mass and velocity. Mathematically, impulse (J) is given by the equation J = mΔv, where m is the mass and Δv is the change in velocity.

In this case, the mass of the point is 1 kg. To find the change in velocity, we need to differentiate the equation for velocity with respect to time (t):

v(t) = dx(t)/dt = d(5 + 0.5t)/dt = 0.5 (m/s²).

Since impulse is the integral of force over time, we can calculate the change in impulse by integrating the change in velocity over time. However, since the mass is constant, we can simply multiply the change in velocity by the mass:

ΔJ = mΔv = 1 kg * 0.5 m/s² = 0.5 kg·m/s.

To find the time it takes for the impulse to change by 4 kg·m/s, we can set up the following equation:

ΔJ = 4 kg·m/s.

Solving for time (t):

0.5 kg·m/s = 4 kg·m/s * t.

t = 0.5 kg·m/s / 4 kg·m/s = 0.125 s.

Therefore, the impulse of the point will change by 4 kg·m/s in approximately 0.125 seconds.

Please note that the given equation for velocity is assumed to be correct based on the information provided.