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An object of mass 500 g, initially at rest, is acted upon by a variable force whose X-component varies with X in the manner shown. The velocities of the object at the points X = 8 m and X = 12 m, would have the respective values of (nearly):

1. 18 m/s and 20.6 m/s
2. 18 m/s and 24.4 m/s
3. 23 m/s and 24.4 m/s
4. 23 m/s and 20.6 m/s

Correct answer: 18 m/s and 24.4 m/s

Solution

The work done by the variable force can be calculated as the area under the force vs. displacement graph. Using the work-energy theorem, the work done equals the change in kinetic energy. From this, the velocities at X = 8 m and X = 12 m are determined.

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