Please show all your work and step. Please write clear

Question

1. Earth = 9.8 meters per second squared [m/s^2]
2. Earth's moon = 1.6 meters per second squared [m/s^2]
3. Mars = 3.7 meters per second squared [m/s^2]

A space probe is built with a mass of 1597 pound-mass [lb_m] before launch on Earth.

The probe is powered by four ion thrusters, each capable of generating 225 millinewtons [mN] of thrust.

How many weeks [wk] will the thrusters have to operate for the probe to reach a velocity of 420 miles per minute [mi/min]? 

The initial velocity of the probe is zero miles per minute [mi/min].

Answer 1

I am assuming that the trip starts in the absence of gravity, because

if it started on Earth then the answer would be "never".

I am also assuming that the fuel burned by the thrusters does not reduce

the mass of the probe.

Let

m = 1597 lb be the mass of the probe,

v = 430 mi/min be the desired increase in velocity,

F = 900 mN = 0.9 N be the total thrust propelling the probe,

a (unknown) be the acceleration of the probe,

t (to be calculated) be the time it takes to reach the velocity v.

By definition of acceleration,

v = at

t = v/a

By Newton's Second Law

a = F/m

t = v/a = vm/F

= 430 mi/min × 1597 lb / (0.9 kgm/s²)

= (430 × 1597 / 0.9) × (mi × lb × s² / (kg × m × min))

= 763011.1 × (1609 × m × 0.45 × kg × s² / (kg × m × 60 × s))

= 763011.1 × 12.0675 × s

= 9208432.9 s

= 15.2 wk