Question

An 82 g arrow is fired from a bow whose string exerts an average force of 95 n on the arrow over a distance of 77 cm. what is the speed of the arrow as it leaves the bow?

Answer 1

You need to find speed, v.
And you (should) recognize the famous F=ma.

We've got data for F and m, so we can find a first!
$a = \frac{f}{m}$
a = 95N / 0.082 kg


Now from a we nees to find v. But how is v and a related?
$a = v \times \frac{dv}{dx}$
where dv is the change in speed (some unknown v minus zero since arrow is initially at rest). dx is the distance where the arrow experiences a force (77 cm!).

Now you know values for a, dv, and dx... you can plug those in and find v!