# Difference between these equations?

1. Nov 20, 2013

### Zondrina

$(1) v_2 = v_1 + a \Delta t$

$(2) v_2^2 = v_1^2 + 2a \Delta d$

My hunch is that $(1)$ represents the final speed in a non-parabolic scenario while $(2)$ is used when the object travels in an arc.

2. Nov 20, 2013

2 is used when an object travels in a straight line.Let's put it this way
$v=u+at$
$v^2=u^2+2as$ (v= final velocity,u = initial velocity)
First equation is just a rearrange of acceleration equation which is
$a=\frac{v-u}{t}$
The second equation is formed by combining the equations
$s=\frac{1}{2}(u+v)t$ and $v=u+at$ (First equation)
These equations are known as Equations of motion.
Each equation has one quantity absent,in equation 1,it's s
In equation 2,It's t.

Yes,the two equations looks similar,because it's subject is v.However,two equations have different quantities.

If for example,u= 0. v= 10m/s .a= 2
Then time taken is 5 sec
and distance traveled is 25m.
What's the problem in this?Does this look similar?Does distance and time look similar?

Note:s is displacement,v and u is velocity.They are not distance and speed
All the equations of motion applies if acceleration is uniform and object move in a straight line

Last edited: Nov 20, 2013
3. Nov 20, 2013

### dauto

But they do produce the same answer and they both apply to uniformly accelerated motion.