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a ball, starting from rest, requires a speed of 10 m/s when a force is applied for a distance of 40 m. if the ball has a mass of 5 kg, what is the force being applied?

Mathematics
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Okay, you can tell this is an energy problem, as opposed to an acceleration problem, because they give you force and distance as opposed to force and time.
So you want to first find the kinetic energy of the ball.\[\Large E_{kinetic}=\frac{1}{2}mv^2\]
Now work is just the change in energy. Since the ball started at rest, it started at 0 energy so\[\Large E_{work} = E_{kinetic} - 0 = E_{kinetic}\]

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Other answers:

Work is force times distance so: \[\Large E_{work}=Fd\]\[\Large F = \frac{1}{d}E_{work}\]
Combine it all together and we get:\[F=\frac{1}{d}\frac{1}{2}mv^2\]Where \(d = 20m\), \(m=5kg\), and \(v=10m/s\)
@raytiller1 I couldn't have made it any easier for you without giving you the answer.
so \[\frac{ 1 }{ 20 }\frac{ 1 }{ 2 } 20(10)\]
You need to square velocity
You also need to look at my formula and understand what I did.

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