Work, Energy, and Power

The work done on an object is given by the function $W(t) = 3t^2 + 2t$, where $W$ is in Joules and $t$ is in seconds. Find the power exerted on the object as a function of time.

A force acting on an object is given by $\vec{F}(x) = (3x^2)\hat{i}$ N, where $x$ is the position in meters. The object's velocity is given by $\vec{v}(t) = (2t)\hat{i}$ m/s. Find the power exerted by the force at $t = 2$ s, assuming $x = t^2$.

The graph of power vs. time is given. What does the area under the curve represent?

What is power defined as, and what are its units?

A force $\vec{F} = (5\hat{i} + 3\hat{j})$ N acts on an object moving with a velocity $\vec{v} = (2\hat{i})$ m/s. What is the instantaneous power delivered by the force?

A car is moving with a velocity of $\vec{v} = (10\hat{i} + 5\hat{j})$ m/s, and a force of $\vec{F} = (2\hat{i} - 1\hat{j})$ N is acting on it. What is the power being delivered to the car?

A work vs. time graph shows that the work done increases from 10 J to 30 J over a time interval of 4 seconds. What is the average power during this interval?

On a work vs. time graph, which time interval indicates the greatest power output?

A work-time graph shows work increasing linearly with time. What does the slope of this graph represent?

An object's velocity is given by $\vec{v}(t) = (3t^2\hat{i} - 2t\hat{j})$ m/s, and it experiences a non-constant force $\vec{F}(t) = (6t\hat{i} + 4\hat{j})$ N. Find the power as a function of time.