Solving for time and final velocity in a basic physics equation

[tomtomgreg]

Homework Statement

So its pretty much just Physics 20 Algebra intro
my teacher assigned us this stuff and i can do it fine i just don't know what to do with the brackets.

d = ( vi + vf / 2 )t

Solve for t, then vf ( can't find any alt codes for small f with the v )

Homework Equations

The Attempt at a Solution

i assumed that after you times the t from the one side and move it to the other that the brackets would then be removed, but a classmate told me that the brackets act as its own variable.

 

[rock.freak667]

d = t(v_i + v_f)/2

because you are multiplying 't' by '(v_i + v_f)/2', you can just divide both sides by ''(v_i + v_f)/2' to make 't' the subject.

 

[CompuChip]

First of all, I assume that you mean
d = (v_i + v_f) / 2 * t,
$$d = \frac{v_i + v_f}{2} t$$
that is: you first add the velocities and divide by 2 (this is actually just the average velocity), and then multiply by the time t.

So you can first "move the t to the other side", actually what you do is divide both the left and the right hand side of the equation by t:
d / t = (v_i + v_f) / 2.

Now you have two options.
1) "Open up" the brackets,

(v_i + v_f) / 2 = v_i / 2 + v_f / 2​

2) Multiply through by 2, so you get

2d/t = (v_i + v_f)​

and now you can remove the brackets from the right hand side because they have become useless.

(This is continuing on your work... if you want to do it the fast way, do what rock said).