Question

To move objects with a variable time step I just have to do:

ship.position += ship.velocity * deltaTime;

But when I try this with:

ship.velocity += ship.power * deltaTime;

I get different results with different time steps. How can I fix this?

EDIT:

I am modelling an object falling to the ground on one axis with a single fixed force (gravity) acting on it.

Answer 1

ship.position = ship.position + ship.velocity * deltaTime + 0.5 * ship.power * deltaTime ^ 2;
ship.velocity += ship.power * deltaTime;

http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/applications/velocity.html

The velocity part of your equations is correct and they must both be updated at every time step.

This all assumes that you have constant power (acceleration) over the deltaTime as pointed out by belisarius.