Question

A 8.56 kg box is constrained to move only along a frictionless x-axis. The box is at rest at the origin when variable force F acts on the mass; the diagram is a graph showing how the force changes with distance. Find the final speed of the mass, in m/s, after it has moved 7 m.

Answer 1

Okay.... As the figure is missing... Here are the steps to solve this question....

We know that work = force * distance

Therefore... You can find work as area under the force - distance graph.... Just find the area under the curve.

After this.... As per work energy theorem.... We know

Work done = change in kinetic energy

As box starts from rest... Initial kinetic energy is zero.

So

W = 0.5mv²

Solve for v, we get

v = sqrt ( W / 0.5m)

Where m is the mass of the box.

That's it....

Here is an example

here,

work done = (6 * 2) + 1/2 * 4 * 3 + 3 *2 + 2 * 2

work done = 28 J

so,

v = sqrt ( 28 / 0.5 * 8.56)

v = 2.557 m/s

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Please let me know if you have any doubt or don't understand any step..... I am here to help.