Question

If a rockets acceleration is given by a=-k/x^2, where x is the distance from the centre of the Earth, and if the rocket starts from rest at the surface of the Earth (radius 6400 km), find an equation for the velocity of the rocket in terms of x.
Answer: v = square root of (k(6400-x))/3200x

Thanks for any help

Answer 1

a(x) = dv/dx = -k/x^2
v(x) = k/x + C
See what you can do with that. But I don't see how the square root will come into play, as there are no fractional powers of x involved.