Question

Определите импульс материальной точки массой 0,5 кг в момент времени 2 с, которая движется вдоль оси ОХ по закону x=2+3t2+2t3 где t - время в секундах, x - координата в метрах

Answer 1

Если V=dx/dt=6t+6t^2, то V(2)=12+24=36м/с; mV=0,5*36=18кг*м/с.

Answer 2

Impulse of a Material Point

The impulse of a material point is defined as the product of its mass and velocity. It represents the change in momentum of the object and is given by the equation:

Impulse = mass × velocity

In this case, we have a material point with a mass of 0.5 kg that is moving along the x-axis according to the equation x = 2 + 3t^2 + 2t^3, where t represents time in seconds and x represents the coordinate in meters.

To determine the impulse of the material point at a specific moment in time, we need to find its velocity at that moment. The velocity can be obtained by taking the derivative of the position equation with respect to time.

Taking the derivative of the position equation, we get:

v = dx/dt = d(2 + 3t^2 + 2t^3)/dt

Simplifying the equation, we have:

v = 6t + 6t^2

Now, we can substitute the given time value of 2 seconds into the velocity equation to find the velocity at that moment:

v = 6(2) + 6(2)^2 = 12 + 24 = 36 m/s

Finally, we can calculate the impulse of the material point by multiplying its mass (0.5 kg) with its velocity (36 m/s):

Impulse = 0.5 kg × 36 m/s = 18 kg·m/s

Therefore, the impulse of the material point with a mass of 0.5 kg at the moment t = 2 seconds is 18 kg·m/s.