Движение материальной точки описывается уравне-
нием х = 5 - 8t + 4t^2
. Приняв ее массу равной 2 кг, найти им-
пульс через 2 с и через 4 с после начала отсчета времени, а
также силу, вызвавшую это изменение импульса.
According to the given equation, the trajectory of the point is given by x(t) = 5 - 8t + 4t^2. Since the mass of the point is 2 kg, the momentum can be calculated as p = mv = 2(5 - 8t + 4t^2) = 10 - 16t + 8t^2. To find the momentum after 2 seconds, we have to substitute t = 2 into the formula, which gives p(2) = 10 - 16(2) + 8(2)^2 = 10 - 32 + 32 = 10 N*s. Similarly, the momentum after 4 seconds is p(4) = 10 - 16(4) + 8(4)^2 = 10 - 64 + 128 = 74 N*s. Finally, the force causing this change in momentum can be found by differentiating the momentum with respect to time, which gives F = dp/dt = -16 + 16t. Substituting t = 2 and t = 4, we get F(2) = -16 + 16(2) = 16 N and F(4) = -16 + 16(4) = 48 N.
