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

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In summary, the problem involves finding the average acceleration of an arrow that is accelerated for a displacement of 75 cm while on the bow, and leaves the bow with a velocity of 75 m/s. The solution involves using kinematic equations to find the average acceleration, assuming a linear variation of acceleration while the arrow is in contact with the bowstring.
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## 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??

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

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

Combine said:
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.

I would approach this problem by first clarifying the units used in the question. The displacement of the arrow is given in centimeters, while the velocity is given in meters per second. It is important to use consistent units in calculations to ensure accuracy.

Assuming the displacement of the arrow is actually 75 meters instead of 75 centimeters, we can calculate the average acceleration using the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time. In this case, vf = 75 m/s, vi = 0 m/s, and t = 0.01 s.

Thus, the average acceleration of the arrow while it is on the bow is 7500 m/s^2. This is a very high acceleration, which is to be expected since the arrow is accelerated to a high velocity in a short amount of time. It is important to note that this acceleration is only applicable while the arrow is on the bow and does not take into account any other forces acting on it after it leaves the bow.

To summarize, the average acceleration of the arrow while it is on the bow is 7500 m/s^2, assuming the displacement is 75 meters and the velocity is 75 m/s. It is important to use consistent units and clarify any uncertainties in the question to obtain an accurate solution.

## 1. What is average acceleration?

Average acceleration is a measure of the change in velocity over a given period of time. It is calculated by dividing the change in velocity by the change in time.

## 2. How is average acceleration different from instantaneous acceleration?

Average acceleration is the average rate of change of velocity over a period of time, while instantaneous acceleration is the rate of change of velocity at a specific moment in time.

## 3. Why is average acceleration important in physics?

Average acceleration is important in physics because it helps us understand how an object's velocity is changing over time, which is crucial in studying motion and forces.

## 4. Can the average acceleration of an object be negative?

Yes, the average acceleration of an object can be negative. This means that the object is slowing down, either in the positive or negative direction depending on its initial velocity.

## 5. How do you calculate average acceleration from a velocity vs. time graph?

To calculate average acceleration from a velocity vs. time graph, you can find the slope of the line connecting the initial and final velocity points. The slope is equal to the average acceleration of the object.

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