00:01
In this problem, we are tasked to find the work done by a force on a particle.
00:06
And we are given the position function for the particle.
00:10
But the force is not a constant.
00:13
So it's a little bit difficult to find it by taking force times displacement.
00:18
In this case, what we're going to do instead is we're going to use the work energy theorem, which says that the work done on an object or system is equal to the change in energy of that object or system.
00:32
And since in this case, it is a single object, which is work is being done on, we can say the change in energy must equal the change in kinetic energy, since kinetic energy is the only kind of energy in object can have.
00:46
In which case then, the work is going to equal the final kinetic energy minus the initial kinetic energy.
00:55
And this thing does not start at rest.
00:57
There is some initial kinetic energy, so we'll have to take that into account.
01:01
In order to find the kinetic energy at any given time, we first need to find the velocity.
01:07
The velocity of this particle should be the derivative of its position function with respect to time...