Questions: A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of 6.20 x 10^5 m/s^2. What is the muzzle velocity of the bullet if the barrel is 52.0 cm long? Use the equation v^2 = v0^2 + 2a(x - x0). 439 m/s 949 m/s 529 m/s 190 m/s

Determine the muzzle velocity of the bullet using the given equation.

Identify the known values.

The average acceleration \( a \) is \( 6.20 \times 10^5 \, \text{m/s}^2 \).
The initial velocity \( v_0 \) is \( 0 \, \text{m/s} \) (since the bullet starts from rest).
The displacement \( x - x_0 \) is \( 52.0 \, \text{cm} = 0.52 \, \text{m} \).

Apply the equation to find the muzzle velocity \( v \).

Using the equation \( v^2 = v_0^2 + 2a(x - x_0) \), substitute the known values:
\[ v^2 = 0^2 + 2 \times 6.20 \times 10^5 \, \text{m/s}^2 \times 0.52 \, \text{m} \]
\[ v^2 = 2 \times 6.20 \times 10^5 \times 0.52 \]
\[ v^2 = 644800 \]
\[ v = \sqrt{644800} \]
\[ v \approx 802.99 \, \text{m/s} \]

The muzzle velocity of the bullet is approximately \( \boxed{803 \, \text{m/s}} \).

The muzzle velocity of the bullet is approximately \( \boxed{803 \, \text{m/s}} \).