Question

Part A: A bullet, initially at rest, is accelerated down the barrel of a gun. It has a velocity of 100.0 m/s as it exits. The barrel of the gun is 1.000 m long. What is the acceleration of the bullet?Part B: How long does it take for the bullet to travel down the barrel of the gun?

Answer 1

We are given that a bullet initially at rest has a final velocity of 100 m/s after accelerating in a barrel that is 1.000 meters long. To determine the acceleration we will use the following equation of motion:

`2ad=v_f^2-v_0^2`

Where:

`\begin{gathered} a=\text{ acceleration} \\ d=\text{ distance} \\ v_f,v_0=\text{ final and initial velocities} \end{gathered}`

Since the bullet starts at rest this means that the initial velocity is zero, therefore:

`2ad=v_f^2`

Now, we solve for the acceleration by dividing both sides by "2d"

`a=(v_f^2)/(2d)`

Plugging in the values:

`a=((100(m)/(s))^2)/(2(1000m))`

Solving the operations:

`a=5000(m)/(s^2)`

Part B. We are asked to determine the time that it takes the bullet to travel the distance. To do that we will use the following formula:

`v_f=v_0+at`

Now, we solve for the time "t". First, we set the initial velocity to zero;

`v_f=at`

Now, we divide both sides by the acceleration:

`(v_f)/(a)=t`

Now, we plug in the values:

`(100(m)/(s))/(5000(m)/(s^2))=t`

Now, we solve the operations:

`0.02s=t`

Therefore, the time is 0.02 seconds.