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

## Homework Statement

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

## Homework Equations

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

## 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)

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

lewando
Homework Helper
Gold Member

The 4th equation looks promising!

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

PeterO
Homework Helper

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