Questions: 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 0.740 m. Determine the acceleration of the bullet (assume a uniform acceleration).

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 0.740 m. Determine the acceleration of the bullet (assume a uniform acceleration).

Transcript text: A bullet leaves a rifle with a muzzle velocity of $521 \mathrm{~m} / \mathrm{s}$. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.740 m . Determine the acceleration of the bullet (assume a uniform acceleration).

Solution

Solution Steps

Step 1: Identify Known Values

We are given:

Final velocity, \( v = 521 \, \text{m/s} \)
Initial velocity, \( u = 0 \, \text{m/s} \) (since the bullet starts from rest)
Distance, \( s = 0.740 \, \text{m} \)

Step 2: Use the Kinematic Equation

To find the acceleration, we use the kinematic equation: \[ v^2 = u^2 + 2as \] Substituting the known values: \[ (521)^2 = 0 + 2a(0.740) \]

Step 3: Solve for Acceleration

Rearrange the equation to solve for \( a \): \[ a = \frac{(521)^2}{2 \times 0.740} \]

Calculate: \[ a = \frac{271441}{1.48} \approx 183400.68 \, \text{m/s}^2 \]

Final Answer

The acceleration of the bullet is \(\boxed{183400.68 \, \text{m/s}^2}\).

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