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"

$a=\frac{v_f^2}{2d}$

Plugging in the values:

$a=\frac{(100\frac{m}{s})^2}{2(1000m)}$

Solving the operations:

$a=5000\frac{m}{s^2}$

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:

$\frac{v_f}{a}=t$

Now, we plug in the values:

$\frac{100\frac{m}{s}}{5000\frac{m}{s^2}}=t$

Now, we solve the operations:

$0.02s=t$

Therefore, the time is 0.02 seconds.