A spacecraft takes 200km after being launched to reach the escape speed from the earth of 11.2km/s.?

Question

Find its average acceleration in term of g

Answer 1

You need the physics equations for constant acceleration that relates velocity, acceleration, and position. (See link below)

Vf^2 = Vi^2 + 2*a*(Xf-Xi)

Vi and Xi are set to zero at the ground. Plug in your final velocity and your final distance, make sure your units match, and calculate your answer:

a = 313.6m/s^2

To get this in terms of Xg, just divide by Earth's gravitational constant.
a = 32.0g

Answer 2

Assuming the spacecraft starts from rest, v0 = 0, then use

dx = (v^2 - v0^2)/(2a) and solve for a

a = (v^2-v0^2)/(2dx)

dx = 200 km = 2x10^5 m, v0 = 0, v = 11.2 km/s = 1.12x10^4 m/s

a = (11.2)^2/(2*200) = 0.3136 km/s^2 = 313.6 m/s^2

g = 9.8 m/s^2 so a/g = 32 or a = 32g