# How to solve for acceleration and position when only time and displacement is known

1. Sep 18, 2012

### frostcloak

1. The problem statement, all variables and given/known data
A rocket blasts off with constant acceleration straight upward. After 3 seconds the rocket is at a height of 80m. (a) what are the magnitude and direction of the rocket's acceleration? (b) what is its velocity at the time

2. Relevant equations

$v=v_0+at$
$v^2=V_0^2+2a\Delta x$
$a=v^2-v_0/(2*x)$
$x=x_0+v_0t+\frac{1}{2}at^2$

3. The attempt at a solution
None, because I was unsure how to proceed as using these equations would result in one unknown (either v or a)

Last edited: Sep 18, 2012
2. Sep 18, 2012

### nasu

Re: How to solve for acceleration and position when only time and displacement is kno

You are missing one equation, the that gives the position as a function of time.

3. Sep 18, 2012

### frostcloak

Re: How to solve for acceleration and position when only time and displacement is kno

4. Sep 18, 2012

### lewando

Re: How to solve for acceleration and position when only time and displacement is kno

The 4th equation looks promising!

5. Sep 18, 2012

### frostcloak

Re: How to solve for acceleration and position when only time and displacement is kno

Yeah i realize that now, plugged in and got acceleration-now i need to just plug acceleration in to get velocity! thanks

6. Sep 19, 2012

### PeterO

Re: How to solve for acceleration and position when only time and displacement is kno

With constant acceleration from rest, the average velocity is one half of the final velocity.

This rocket covered 80m in 3 seconds, so average velocity is easy to find. Double that and you have the final velocity.

Once you have that final velocity you can easily get acceleration since you know by how much the velocity changed in 3 seconds.