Nasa has developed deep-space 1 (ds-1), a spacecraft that is scheduled to rendezvous with the asteroid named 1992 kd (which orbi
ts 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?
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
