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Problem 43 Hard Difficulty

The position of an object with mass $ m $ at time $ t $ is $ \textbf{r}(t) = at^2 \, \textbf{i} + bt^3 \, \textbf{j} $, $ 0 \leqslant t \leqslant 1 $.

(a) What is the force acting on the object at time $ t $?
(b) What is the work done by the force during the time interval $ 0 \leqslant t \leqslant 1 $?

Answer

(a) $2 m a$ i $+6 m b t$ j, $0 \leq t \leq 1$
(b) $2 m a^{2}+\frac{9}{2} m b^{2}$

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Video Transcript

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