if you acceleration doubled?

Question

let's say every three seconds, starting at 2 mph, would the g-force increase as well as your speed. i would suppose it would, but is there a ratio where the g-force stays the same throughout acceleration

Answer 1

G = a/g; where G is the number of g's in an acceleration of a. For example, if you're accelerating at 64.4 ft/sec^2, you are pulling 2G's = 64.4/32.2. So assume a(0) is the acceleration at time t = 0, the beginning. Now at t = 3 sec, we have a(3) = 2a(0), which means it doubled after your three seconds elapsed.

So the change in G's is G(3) - G(0) = [2a(0) - a(0)]/g = a(0)/g = G(0). Which means G(3) = 2G(0); that is, when you double the acceleration, you double the G's. In this context, there is no limit (there are energy/mass limits in relativity however). Thus, the G's do not level off and stay the same as acceleration increases.

Answer 2

If you double your speed every three seconds, v=2*2^(t/3). Acceleration is dv/dt = 2*ln(2)*2^(x/3)/3 which is not constant. Any ratio of increasing speed must increase acceleration also. The only constant acceleration occurs when the speed increase is linear, such as v=10t.