Solving a Trolley Acceleration Dilemma: Power vs. Time

[al_201314]

Hi guys,

I've got one question couldn't figure out over the night. Here goes:

A trolley is accelerated by a constant force from a motor. If friction forces can be neglected, what would the graph of the power of the motor against time be like?

My answer is a straight horizontal line for some value of P. The answer I was given was a straight line graph from the origin with a postiive gradient. Why is this so? My reasoning is that the motor supplies a constant force which would necessary mean the rate of doing work is constant?

Thanks!

 

[Doc Al]

My reasoning is that the motor supplies a constant force which would necessary mean the rate of doing work is constant?

While the force is constant, the speed is increasing. The work required to move the trolley a given distance will remain the same, but as the trolley speeds up that same work must be done in a shorter amount of time.

 

[al_201314]

Thanks Doc Al it didn't occur to me.