If the first stage provides a thrust of 5.25 mega-newtons [MN] and the space shuttle has a mass of 4,470,000 pound-mass [lbm], what is the acceleration of the spacecraft in miles per hour squared [mi/h2]

20,861.65 mi/h²

Explanation:

We convert  4,470,000 pound-mass [lbm], to kg. Since  2.205 lbm = 1 kg, then 4,470,000 lbm = 4,470,000 lbm × 1 kg/2.205 = 2,027,210.88 kg

Since Force , F = ma where m = mass and a = acceleration, and our force of thrust , F = 5.25 MN = 5,250,000 N and or mass = mass of spacecraft = 2,027,210.88 kg, we then find the acceleration, a.

a = F/m = 5,250,000 N/2,027,210.88 kg = 2.59 m/s².

We now convert this acceleration into miles per hour. Since 1 mile = 1609 meters and 60 × 60 s = 1 hour ⇒ 3600 s = 1 hour, Our conversion factor for meter to mile is 1 mile/1609 m and that for second to hour is 3600 s/1 hour. We square the conversion factor for the time so we have (3600 s/1 hour)².

Multiplying both conversion factors with our acceleration, we have

a = 2.59 m/s²

= 2.59 m/s² × 1 mile/1609 m × (3600 s/1 hour)²

= 33566440/1609 miles/hour²

= 20,861.65 mi/h²

= 20,861.65 miles per hour squared

answer: 31, 5556. 952 seconds