A stationary 1.67-kg object is struck by a stick. The object experiences a horizontal force given by F = at - bt2, where t is the time in milliseconds from the instant the stick first contacts the object. If a = 1500 N/(ms) and b = 20 N/(ms)², what is the speed of the object just after it comes away from the stick at t = 2.74 ms? A) 3.3 m/s B) 22 m/s C) 3.7 m/s D) 25 m/s

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Quizplus · Accepted Answer

Impulse = change in momentum$$J = mv_f - mv_i$$$$J = \int_0^{2.74} (1500t - 20t^2)dt$$$$J = [750t^2 - \frac{20t^3}{3}]_0^{2.74}$$$$J = 4.46 	ext{ Ns}$$$$4.46 = (1.67)v_f$$$$v_f = 3.3 	ext{ m/s}$$

A Stationary 1