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Problem 41 Easy Difficulty

A single force acts on a 3.0 $\mathrm{kg}$ particle-like object whose position is given by $x=3.0 t-4.0 t^{2}+1.0 t^{3},$ with $x$ in meters and $t$ in
seconds. Find the work done by the force from $t=0$ to $t=4.0 \mathrm{s}$

Answer

$=528 \mathrm{J}$

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Video Transcript

well done by the force it's given by changing can take energy. And this is equal to one over two m into we a final velocity squared minus initial velocity square masses keeping. So we'll find a final lost in an initial losses. We can find it from the given position, uh, and given position we do you rate the you in position with respect to time. The extra have Aditi. This gives us we need to be three minus state times T plus three t square 40 years ago to zero, which will become our initial velocity. We I So we I we get here is a three meter per second forties equal to four seconds. Then we f we get here is a 19 meter for second. Well, substitute these values. Maybe I will come here and be careful. Come here. After substituting those values, we get our changing dynamic energy, which is a good work done to be 5 28 Jules

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