A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m in 0.003 seconds. Determine the acceleration of the bullet.

Question

A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m in 0.003 seconds. Determine the acceleration of the bullet.

So I basically used the formula:

Change in position= (Initial velocity*Change in time) + (Acceleration((Change in time)^2))/2) to solve for a, my acceleration.

So 0.840= 521(0.003) + 0.000009/2 (a)

So 0.840- 1.563= -0.723= 0.000009/2 (a)

-0.723*2= -1.446= 0.000009a

-1.446/0.000009 = -160666.6667= a

so my acceleration= -160666.6667

But i'm confused. i thought the bullet should be accelerating logically, not decelerating. am i even right? Where did I go wrong?

Answer 1

never mind, i think i found my mistake. 521m/s is the final velocity, not initial. thanks guys

Answer 2

Acceleration is any change in velocity. You can slow down, speed up, or turn. BTW, try not to use the term deceleration. It's best to use negative acceleration.

Answer 3

You are correct in thinking that the bullet should be accelerating, not decelerating. It seems that there is a mistake in your calculation.

Let's go through the steps again to determine the acceleration of the bullet:

1. Start with the formula:
Change in position = (Initial velocity * Change in time) + (Acceleration * (Change in time)^2)/2

2. Rearrange the formula to solve for acceleration (a):
Acceleration = 2 * (Change in position - (Initial velocity * Change in time)) / (Change in time)^2

3. Substitute the known values:
Change in position = 0.840 m
Initial velocity = 521 m/s
Change in time = 0.003 s

Acceleration = 2 * (0.840 - (521 * 0.003)) / (0.003)^2

4. Simplify the equation:
Acceleration = 2 * (0.840 - 1.563) / (0.003)^2

Acceleration = -1.446 / 0.000009

5. Calculate the acceleration:
Acceleration = -160666.6667 m/s^2

From your calculation, it seems like there is a sign error somewhere. It is possible that you made a mistake when subtracting the product of the initial velocity and the change in time from the change in position. Double-check your calculation to ensure that the values are correct and that you are subtracting the correct term.

Once you find the correct value for the change in position, the calculation should result in a positive acceleration, indicating that the bullet is indeed accelerating.