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Problem 6 Easy Difficulty

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 $5.0-\mathrm{kg}$ projectile from rest to a speed of $4.0 \times 10^{3} \mathrm{m} / \mathrm{s}$ . The net force accelerating the projectile is $4.9 \times 10^{5} \mathrm{N}$ . How much time is required for the projectile to come up to speed?

Answer

0.041 $\mathrm{s}$

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Video Transcript

in this question that candle fires a projectile by applying force or 4.9 times 10 to the fifth. Newton's on it, and by doing that it gave off, making its velocity change from 0 to 4 times 10 to the third meter. Spare. Second. Doing that, the man's off. This projectile is it was Christ kilograms catheter mind. How much time does it take? What's the velocity to change from 0 to 4 times 10 to the turn? We begin by remembering that decorations behind as a variation, velocity divided by the time it takes for the variation toe occur. Then we can sew for the tea here by sending this time to the underside of this term to the other side. This gives us Dougherty, you close to doctors. They divided by declaration. And this is the equation. We will be using this question. The variation in the velocity is requested for time. Stand to the third, and the only thing we don't know now is the acceleration. For that. We can use Newton's second law. We say that then that force is the coast to the mass off the projectile times acceleration. The net force is it goes to 4.9 times 10 to the fifth. The mass is five kilograms on exploration. We're calculating right now. Then, by sending this term to the other side, you get 4.9 times. Stand to this divided by five as our acceleration. Then we can plug in these results in the equation. By doing that, we got Deputy is because the four times stand toe to toe divided by four point tonight. Timestamp Mrs United by five. And this is the coast too. Five times four thanks then occurred, divided by 4 29 constant. And then we got the following five times four is 20 needed divided by 4.9. And here we have 10 to the third minus size because we have 10 to the third in the numerator and tend to the seat on the denominator. So his results in 20 divided by 4.9. I understand this truth, which is true. Do vital my apartment nine times 10 miners one. Finally, this gives the time of approximately the 0.4 times Stan to the miners one which is close to 0.4 seconds