Question

The barrel of a rifle has a length of 0.884 m. A bullet leaves the muzzle of a rifle with a speed of 623 m/s. What is the acceleration of the bullet while in the barrel? (Note: Assume constant acceleration for this problem.)

A) The acceleration is 706.05 m/s².
B) The acceleration is 140.93 m/s².
C) The acceleration is 817.65 m/s².
D) The acceleration is 628.65 m/s².

Answer 1

The acceleration of the bullet while in the barrel is 706.05 m/s².

Step-by-step explanation:

The acceleration of the bullet while in the barrel can be determined using the kinematic equation:

v = u + at

where v is the final velocity, u is the initial velocity (0 m/s in this case), a is the acceleration, and t is the time.

The length of the barrel, 0.884 m, corresponds to the displacement of the bullet, and since the initial velocity is 0 m/s, the equation becomes:

0.884 = 0 + (1/2)at^2

Simplifying the equation, we get:

a = (2 * 0.884) / t^2 = 2.768 / t^2

Given that the bullet leaves the muzzle of the rifle with a speed of 623 m/s, we can find the time it takes to travel through the barrel using the formula:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Solving for t, we have:

623 = 0 + at

t = 623 / a

Substituting this value of t into the equation for acceleration, we get:

a = 2.768 / (623 / a)^2

Simplifying this equation, we find that the acceleration of the bullet while in the barrel is 706.05 m/s².