CP CALC? A mysterious rocket-propelled object of mass 45.0 kg is initially at rest in the middle of the horizontal, friction-less surface of an ice-covered lake. Then a force directed east and with magnitude F(t) = (16.8 N/s) t is applied. How far does the object travel in the first 5.00 s after the force is applied?

Solution 61P Given a time independent force F(t),is applied on a mysterious rocket of mass m.after finding the acceleration a,using newton’s laws of motion,we will find out the distance traveled by the rocket in a given time.here we will use method of integration. Acceleration a(t) = F/m = (16.8 N/s/45 kg) t * 0.373 m/s 3* t Then 3 2 v(t) =a(t)dt = 0.187 m/s * t + c Since v(0) = 0, c = 0. 3 3 s(t) =v(t)dt = 0.0622 m/s * t + c Since x(0) = 0,c = 0 again. 3 2 Hence s(5.00 s) = 0.0622 m/s * (5.00) s = 15.5 m.