# Distance in time at acceleration

1. Nov 2, 2006

### dirty_d

what is the formula to find the time it takes for an object to travel a distance at a certain acceleration from a certain initial velocity? I think i've figured out it without taking into account the initial v which would be t = squareroot( (d * 2) / a), i think.... but i'm not sure how to fit the initial velocity in there.

2. Nov 2, 2006

### Cyrus

Can you show some work?

3. Nov 2, 2006

Start off with the equation $$d = d_{0}+v_{0}t+\frac{1}{2}at^2$$. The equation you got would be valid for d0 = v0 = 0.

Last edited: Nov 2, 2006
4. Nov 2, 2006

### dirty_d

radou i have no idea how to rearrange that formula, cyrusabdollahi, an example would be if a rocket is in space with the engine off traveling at 1000 m/s towards the sun and then turns the engine on and starts accelerating at 100 m/s/s in the same direction how long would it take to travel 1000 km towards the sun from when it starts accelerating.

5. Nov 2, 2006

### Cyrus

What is your level of math?

6. Nov 2, 2006

level = low

7. Nov 2, 2006

anybody...

8. Nov 2, 2006

### dirty_d

this works i dunno if it can be simplified any,

t = d / ((sqrt(pow(v0, 2) + 2 * a * d) + v0) / 2)