the tranquilizer projectile accelerates from rest to a speed of 521 m/s while traveling through the barrel of gun, which is .740 meter long. assuming uniform acceleratiin, determine the acceleration of the peojectile

To find the acceleration of the tranquilizer projectile, we can use one of the equations of motion, specifically the equation that relates acceleration to initial velocity, final velocity, and distance traveled:

\[
v^2 = u^2 + 2as
\]

Where:
- \( v \) is the final velocity (\( 521 \) m/s),
- \( u \) is the initial velocity (\( 0 \) m/s, since it starts from rest),
- \( a \) is the acceleration (which we want to find),
- \( s \) is the distance traveled (\( 0.740 \) meters).

Plugging in the given values:

\[
521^2 = 0^2 + 2 \cdot a \cdot 0.740
\]

\[
271441 = 1.48a
\]

Now, solve for \( a \):

\[
a = \frac{271441}{1.48}
\]

\[
a \approx 183000 \, \text{m/s}^2
\]

The acceleration of the projectile is approximately \( 183,000 \) m/s\(^2\).

Would you like more details, or do you have any questions? 

### Here are 5 related questions that expand on this information:

1. What would be the time taken by the projectile to travel through the barrel if the acceleration is \( 183,000 \) m/s\(^2\)?
2. How would the acceleration change if the barrel length were doubled?
3. What impact does barrel length have on the final speed of a projectile assuming uniform acceleration?
4. What would be the final velocity if the projectile accelerates at the same rate but starts from an initial velocity of \( 100 \) m/s?
5. How does non-uniform acceleration affect the calculations of final speed and acceleration?

**Tip:** Always use consistent units (like meters and seconds) when working with physics equations to avoid errors in calculations.

Learn how to determine the acceleration of a projectile in a gun barrel that reaches a final velocity of 521 m/s. This physics problem involves uniform acceleration and uses the equation of motion for distance, initial and final velocities. Suitable for high school physics students.

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