Question

Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 5.6-kg projectile from rest to a speed of 3.5 × 103 m/s. The net force accelerating the projectile is 2.5 × 105 N. How much time is required for the projectile to come up to speed?

Answer 1

Answer:

7.84 s

Explanation:

Ok, one step at a time. We know the mass of the projectile, we know the force. Acceleration is easily obtained from Newton second law:

$\vec F = m\vec a$$2.5\times 10^5 = 5.6a \rightarrow a = (2.5/5.6) \times 10^5 = 4.46 \times 10^4 ms^-^2$.

At this point, we know the acceleration, we know initial and final velocity, we can time the ammount of time it took to get there.

$v= v_0 +at \rightarrow 3.5\times10^3 = 0 + 4.46\times10^4 t\\t= \frac{3.5\times10^3}{4.46\times10^4} = 7.84 s$