Answer:
Givens:
We know that kinetic energy is: 

So, we just need to calculate the speed. We have the equation of the movement, if we derivate that expression, we'll have the speed:

Which is the speed at any time <em>t.</em>
Now, we replace the expression to find the kinetic energy at any time <em>t:</em>


So, this is the kinetic energy at energy at any time <em>t.</em>
Through derivation we can find the acceleration and force at any time <em>t:</em>
<em> </em>
</em>
Also, we know that 
Replacing values: 
The power is define as the product of the force and the velocity:

At last, we now that the work is define as: 
So, we just replace the force, and integrate it between <em>t=0 </em>and<em> t=2 sec.</em>
<em>![W=\int _{0}^{2} 48t(6t^{2}+1)dt\\W=\int_{0}^{2} (288t^{3}+48t)dt\\W= \frac{288t^{4} }{4}+\frac{48t^{2}}{2} ]_{0}^{2} \\W= 72t^{4}+24t^{2}]_{0}^{2}\\W=72(2)^{4}+24(2)^{2}\\W= 1152 + 96=1248 \ J](https://tex.z-dn.net/?f=W%3D%5Cint%20_%7B0%7D%5E%7B2%7D%2048t%286t%5E%7B2%7D%2B1%29dt%5C%5CW%3D%5Cint_%7B0%7D%5E%7B2%7D%20%28288t%5E%7B3%7D%2B48t%29dt%5C%5CW%3D%20%5Cfrac%7B288t%5E%7B4%7D%20%7D%7B4%7D%2B%5Cfrac%7B48t%5E%7B2%7D%7D%7B2%7D%20%5D_%7B0%7D%5E%7B2%7D%20%5C%5CW%3D%2072t%5E%7B4%7D%2B24t%5E%7B2%7D%5D_%7B0%7D%5E%7B2%7D%5C%5CW%3D72%282%29%5E%7B4%7D%2B24%282%29%5E%7B2%7D%5C%5CW%3D%201152%20%2B%2096%3D1248%20%5C%20J) </em>
</em>