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

7.84 s

Step-by-step 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* 10^5 = 5.6a \rightarrow a = (2.5/5.6) * 10^5 = 4.46 * 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*10^3 = 0 + 4.46*10^4 t\\t= (3.5*10^3)/(4.46*10^4) = 7.84 s`