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 5.0-kg projectile from rest to a speed of 4.0 × 103 m/s. The net force accelerating the projectile is 4.9 × 105 n. How much time is required for the projectile to come up to speed?

Answer 1

The time taken by the projectile to reach the required speed is 41 ms.

Calculate the acceleration  a of the projectile of mass m, using Newton's second law.

$F=ma$

Substitute 5 kg for m and 4.9×10⁵N for F, the force needed for acceleration.

$F=ma\\ a=\frac{F}{m} \\ =\frac{(4.9*10^5 N)}{5 kg} \\ =9.8*10^4 m/s^2$

Use the equation of motion $v=u+at$ to determine the time taken by the projectile to reach a speed v from rest under the acceleration calculated.

$t=\frac{v-u}{a}$

Substitute 4.0×10³m/s for v, 0 for u and 9.8×10⁴m/s² for a.

$t=\frac{v-u}{a}\\ =\frac{(4.0*10^3 m/s)-0}{(9.8*10^4m/s^2)} \\ =0.0408 s\\ =41 ms$

The time taken to reach the required speed is 41 ms.