Question

Nasa has developed deep-space 1 (ds-1), a spacecraft that is scheduled to rendezvous with the asteroid named 1992 kd (which orbits the sun millions of miles from the earth). the propulsion system of ds-1 works by ejecting high-speed argon ions out the rear of the engine. the engine slowly increases the velocity of ds-1 by about +9.23 m/s per day. (a) how many days will it take to increase the velocity of ds-1 by +3440 m/s? (b) what is the acceleration of ds-1?

Answer 1

I can't give an exact number if the original velocity of ds-1 is not given. In that case, the final answer should just be in terms of an equation. Let's denote the original velocity to be v₀ and the days to be d.

Part a.)
v = v₀ + 9.23d
3440 = v₀ + 9.23d
9.23d = 3,440 - v₀
d = (3,440 - v₀)/9.23

Part b.)

The acceleration is the change in velocity per unit time. So, that would be 9.23 m/s per day. Since there are 86,400 s in a day:

a = 9.23 m/s / day * 1 day/ 86,400 s
a = 0.0001068 m/s²