What to do with a mathematic equation

[RabbitWho]

Homework Statement

A ball is thrown upwards at a speed of 29.4m/s
Where is it 4 seconds after being released.

Homework Equations

d[/B]=v₀t+1/2at²

So I understand what the letters all stand for because that information is explained, but I don't know what to do with it.

The Attempt at a Solution

The answer is 39.2. I don't know how or why because I don't understand basic mathematics notation. If a and t are next to each other like that am I supposed to multiply them by each other?
But what about the half? Is it half of a (14.2), or is it half of a multiplied by t (58.8)? Then I multiply one of those numbers by itself because of the ².. If I see a bunch of things together like that how do i know whether you multiply something by the next thing or the next 2 things or work with the others first then go back to that or... ?
so
d=0 (speed at beginning)x4
So that first part is just 0, right, i can ignore it? x 14.2 x 14.2 = 201.64... Argh I'm

Also, can someone tell me where the half comes from in the equation?If someone could do the sum with all (and i mean all!) the rough work I think I'd be able to pick up what I am supposed to do. I used to be able to do this but I haven't done anything except add and subtract in 12 years.

 

[Fancypen]

This seems like a nice Free-Fall physics problem. You have an upward initial velocity of 29.4 m/s and as it travels up, the only force acting on it (for this problem) is the force of gravity at 9.8 m/s/s downward (depending on your frame of reference).

The equation you used will solve the problem. This is a variation of some other constant acceleration equations.

d = distance traveled (your soln)
vo = initial velocity
t = time
a = acceleration (gravity in this case)
t^2 = time (again)

If a and t are next to each other and you have values for each, then yes, multiply them together. 1/2 x 9.8 x 4^2 can be evaluated in any order because multiplication is commutative (as long as you evaluate the 4^2 first).

I don't know how to derive this equation or others like it but I believe it comes from integrating... something... lol sorry can't be more helpful.

I JUST took mechanics so if anyone sees any flaws, please help us both out.

p.s. Maybe review some algebra axioms, so evaluating algebraic equations will be much easier. If you have the time check out, daabz.com and go over his algebrea 46 (I think it's 46) class. It's a proof based algebra class that covers the main axioms. I am in calc 3, linear algebra, discrete math atm, but I took this class on my own recently and it has sharpened my skills exponentially! He was my calc 2 prof.; very cool guy.
Chris

 

[Doc Al]

If a and t are next to each other like that am I supposed to multiply them by each other?

When "things" (numbers and other factors) are next to each other, that means multiply them together.

So 1/2at² means: (1/2) X (a) X (t²)

Note: The speed at the beginning is not zero! You are given the speed.

Note 2: Take care with signs. Use + for up and - for down. (Given that, what would you use for the acceleration a?)

 

[RabbitWho]

So 1/2at2 means: (1/2) X (a) X (t2)

Sorry about getting the starting speed wrong, I was thinking about earlier when the ball fell off something, so its starting speed was 0 then. I also had the speed and the acceleration mixed up, the acceleration must be -9.8m/s because it is fighting gravity.So half times a is -4.9.
4.9 x (4x4) = -78.4

Then the first half

d=29.4 x 4 + -78.4
d = 117.6 - 78.4

= 39.2
HA HA I DID IT :D

Thanks and thanks for your patience :)
My immense sense of satisfaction is quite disproportionate to the objective difficulty of the question, but I am still going to enjoy it :)

 

[Doc Al]

Nice!