How Is Average Acceleration Calculated for an Arrow on a Bow?

[Combine]

Homework Statement

I will just try to post the whole questions, maybe my idiot eyes missed something...

an arrow is accelerated for a displacement of 75cm [fwd]
while it is on the bow, if the arrow leaves the bow at a velocity of 75m/s [fwd]
what is it's average acceleration while it's on the bow

Homework Equations

t = displacement/ velocity
a = velocity/time

The Attempt at a Solution

75 cm -> .75
0.75 / 75 = 0.01s
disp = 75m

t = 75/0.75 = 100s
velocity = 75m/s

a = velocity / time
time = displacement + velocity / velocity
acceleration = velocity/(disp/velocity) = vecloity / 0.01 = 7500 WTH??

 

[SteamKing]

The arrow leaves the bow with a velocity of 75 m/s, but its initial velocity = 0 m/s

 

[Combine]

ya it should be, according to logic I guess lol
just I've been having a lot of trouble trying to figure out the average acceleration

 

[PhanthomJay]

ya it should be, according to logic I guess lol
just I've been having a lot of trouble trying to figure out the average acceleration

Average acceleration is the change in velocity divided by the change in time. You are not given the time. So you must assume a linear variation of acceleration while the arrow is in contact with the bowstring (it behaves like a spring), in which case you can use the standard kinematic equations to solve for the average acceleration.