A particle starts from rest and is acted on by a net force that does work at a rate that is proportional to the time t. The speed of the particle is proportional to √t.
Work is a change in kinetic energy, it should be noted. Power will therefore be determined as follows:
Power = Work / Time = force × velocity
Work = the change in kinetic energy = 1/2 mv2
If work is proportional to time:
W = t
1/2 mv2 = t
v2 = t
v (speed) = √t
Speed is the rate and direction of an object's movement, as well as the rate and duration at which an object is moving along a path. In all other positions, speed is a scalar value while pace is a vector.
Power is inversely related to t. Because the force is constant, the velocity will be a function of t. As a result, the particle's speed is proportional to √t.
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