Average acceleration of an arrow by a bow

[rxhim631]

Homework Statement

An arrow is accelerated for a distance of 75 cm [fwd] while it is on the bow. If the arrow leaves the bow at a velocity of 75 m/s [fwd], what is the average acceleration while on the bow?

Relevant Equations

Distance= (Intial Velocity + Final Velocity / 2) Time

Acceleration = (Final Velocity + Intial Velocity) / Time

Distance= (Intial Velocity + Final Velocity / 2) Time

0.75 = (0+75 / 2) Time

0.75 = (37.5) Time

0.02 seconds = Time

Acceleration = (Final Velocity + Intial Velocity) / Time

Acceleration = (75 - 0) / 0.02

Acceleration = 3750 m/s2

Idk if this is correct can someone help pls.

 

[TSny]

Relevant Equations:: Distance= (Intial Velocity + Final Velocity / 2) Time

This equation is not true in general. It is valid for the case of constant acceleration along a line. A bow string will exert a force on the arrow that decreases in strength as the string relaxes. So, the arrow will have a non-constant acceleration while it is being pushed by the string. This means that the above equation is not actually valid. However, it could be that this is an exercise where they want you to treat the arrow as having a constant acceleration. Otherwise, I don't think there is enough information to work the problem.

Another somewhat picky point is that you need to include additional parentheses to conform to standard conventions for "order of operations":

Distance= ((Intial Velocity + Final Velocity) / 2) Time

Acceleration = (Final Velocity + Intial Velocity) / Time

Did you mean to type a minus sign instead of the plus sign?

Your calculation looks OK. I think your final answer is correct if we can assume that the acceleration is constant.

 

[haruspex]

If we make the reasonable assumption that the motion is approximately SHM, the average acceleration is $4/\pi$ times as much.