A rail gun uses electromagnetic energy to accelerate objects quickly over a short distance. In an experiment, a 2.00 kg projectile remains on the rails of the gun for only 2.10x10^-2 s, but in that time it goes from rest to a velocity of 4.00×10^3 m/s. What is the average acceleration of the projectile?
To find the average acceleration of the projectile, you can use the equation:
Average acceleration = (Final velocity - Initial velocity) / Time
In this case, the initial velocity is zero because the projectile starts from rest. The final velocity is given as 4.00 × 10^3 m/s, and the time is given as 2.10 × 10^-2 s.
Substituting the given values into the equation:
Average acceleration = (4.00 × 10^3 m/s - 0 m/s) / (2.10 × 10^-2 s)
To simplify the calculation, you can rewrite the powers of 10:
Average acceleration = (4.00 × 10^3) / (2.10 × 10^-2)
Now, divide the numerator and denominator by 2.10:
Average acceleration = (4.00 × 10^3) / (2.10) × (1 / 10^-2)
Simplifying further:
Average acceleration = (4.00 × 10^3) / (2.10) × (10^2)
Now, multiply the numerator and denominator:
Average acceleration = 2.00 × (10^3) × (10^2) / 2.10
The product of the powers of 10 is equal to adding their exponents:
Average acceleration = 2.00 × 10^(3+2) / 2.10
Finally, calculate the average acceleration:
Average acceleration = 2.00 × 10^5 / 2.10
Divide the numerator by the denominator:
Average acceleration ≈ 95,238 m/s^2
Therefore, the average acceleration of the projectile is approximately 95,238 m/s^2.