Work-energy Theorem

Question

Net work on a 4 kg body is 80 J from rest. Final speed?

RankGuru · Accepted Answer

1. **Work-Energy Theorem**: The net work done on an object is equal to its change in kinetic energy ($W_{net} = \Delta K$).
2. **Constraint**: Since it starts from rest, $K_{initial} = 0$.
3. **Formula**: $W_{net} = \frac{1}{2} m v^2$.
4. **Solve for v**:
   - $v^2 = \frac{2 W}{m}$
   - $v = \sqrt{\frac{2 	imes 80}{4}} = \sqrt{\frac{160}{4}} = \sqrt{40}$.
5. **Calculation**: $\sqrt{40} \approx 6.3245$ m/s.
6. **Result**: Final speed is **$6.32$ m/s**.

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