# Calculating the final velocity?

1. Apr 18, 2012

### mailhiot

If an object starts with an initial velocity of 0, and has a velocity of 1.07 m/s after 20 cm, what is the velocity at 1 meter, assuming a constant acceleration? I do not know how long it takes to travel the full 1 meter. All I know is that after 20 cm the velocity was 1.07 m/s and it took 177 miliseconds to travel the 20 cm.

2. Apr 18, 2012

### victor.raum

Firstly, recall the general relationship between a constant force and a change in kinetic energy: $$F\cdot\Delta x = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2$$

In this case you have $v_1=0$, so that comes out to simply $$F\cdot\Delta x = \frac{1}{2}mv_2^2$$

Now find out what $F$ is by rearranging this to

$$F = \frac{\frac{1}{2}mv_2^2}{\Delta x}$$

Plug in any available velocity and corresponding location into the above, and you'll find the constant force.

Next rearrange to instead solve for the velocity as a function of distance

$$\sqrt{\frac{2F\cdot\Delta x}{m}} = v_2$$

And then flip that, because it just looks better flipped:

$$v_2 = \sqrt{\frac{2F\cdot\Delta x}{m}}$$

Plug in a value of 1 meter for the distance, and you'll find your velocity at that location.