A machine does work at a rate given by P=ct^2, where c= 12 W/s^2 and t is time.

Question

A machine does work at a rate given by P=ct^2, where c= 12 W/s^2 and t is time. Find the Work done by the machine between 11s and 22s. Honestly, I have no idea where to start. I feel like I am way over thinking things. I keep getting 42J, but that isn't right.
Step by step solution would be much appreciated! A machine does work at a rate given by P=ct^2, where c= 12 W/s^2 and t is time. Find the Work done by the machine between 11s and 22s. Honestly, I have no idea where to start. I feel like I am way over thinking things. I keep getting 42J, but that isn't right.
Step by step solution would be much appreciated! A machine does work at a rate given by P=ct^2, where c= 12 W/s^2 and t is time. Find the Work done by the machine between 11s and 22s. Honestly, I have no idea where to start. I feel like I am way over thinking things. I keep getting 42J, but that isn't right.
Step by step solution would be much appreciated! A machine does work at a rate given by P=ct^2, where c= 12 W/s^2 and t is time. Find the Work done by the machine between 11s and 22s. Honestly, I have no idea where to start. I feel like I am way over thinking things. I keep getting 42J, but that isn't right.
Step by step solution would be much appreciated!

Explanation / Answer

power, P = dW/dt

==>dw = p*dt

W = integral dW (t is changing from 11s 22s)

= integral p*dt (t is changing from 11s 22s)


= integral c*t^2*dt (t is changing from 11s 22s)


= c*t^3/3 (t is changing from 11s 22s)

= (12/3)*(22^3-11^3)

= 37268 J

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