# Motion Formulas

1. Sep 2, 2006

hey,
I’ve been wondering for quite sometime now that if I am given values for displacement, time, and final velocity if it were able to calculate the acceleration and the initial velocity? I have been trying to rearrange the formulas:

$$v = u + at$$

$$v^2 = u^2 + 2as$$

$$s = ut + .5at^2$$

but have been unsuccessful. I would like to know if it were possible to calculate the unknowns using the values given, thanks,

2. Sep 2, 2006

### Päällikkö

From the first equation:
$$a = \frac{v-u}{t}$$

Substitute to the third.

3. Sep 2, 2006

### Random333

That still wouldn't be helpful seeing the initial velocity is unknown, what would be helpful is another equation:

$$s = t \frac{v+u}{2}$$

And transpose to give

$$u = \frac{2s}{t} - v$$

There is another way to calculate a as well using the 3rd formula, make ut = vt and - the $$.5at^2$$. Which will give you the right answer, you can test it by substituing fake values in.

4. Sep 2, 2006

### Päällikkö

Sure it would.
Making the substitution:

$$s = ut + \frac{1}{2}(v-u)t$$

$$u = 2 \frac{s}{t} - v$$

5. Sep 2, 2006

### Random333

Ah, of course.

6. Sep 2, 2006