The 100 kg box shown above is being pulled along the x-axis by a student. The bo

Question

The 100 kg box shown above is being pulled along the x-axis by a student. The box slides across a rough surface, and its position x varies with time t according to the equation x= 0.5 t^3 + 2t, where x is in meters an is in seconds determine the speed of the box at time t=0s determine the following as functions of time t. The kinetic energy of the box the net force acting on the box the power being delivered to the box calculate the net work done on the box in the interval r=0 to t=2s. Indicate below whether the work done on the box by the student in the interval t = 0 to t = 2s would be greater than, less than, or equal to die answer in pan (c). -Greater than _Less than _Equal to Justify your answer

Explanation / Answer

a: 2 m/s

b.i:K.E=1/2mv^{2}=1/2 (100)(1.5t^{2}+2)^2 J

b.ii: F=ma=(100)(3t)

b.iii:P=F.v=(300t)(1.5t^{2}+2)

c: Net work done between t=0s and t=2s is given by int F.dx=int P.dt=int(450t^{2}+600)dt=2400.

d: Net work done by the student would be greater than the net work, because friction opposes the motion, and does negative work.

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