Can someone help me with Physics?

Question

Ok, I'm a little lost right now. In what case do you use the formulas:

v^2 = v0^2 + 2a(x-x0)

and

(average) v = (v + v0)/ 2

Answer 1

v^2 = v0^2 + 2a(x-x0)

v^2: the velocity squared

v0^2: initial velocity

2a: acceleration times two

(x-x0): final distance - initial distance  

Used to find velocity.



----------------------

(average) v: average velocity

(v + v0): final velocity + initial velocity

/2: divide (v + v0) by two

Used to find average velocity.

Answer 2

v² = v₀² + 2aΔx

That's one of the kinematic equations.  There are 5. The kinematic variables (in 1D) are:

v₀ = initial velocity

v = final velocity

a = acceleration

Δx = displacement

t = time

The 5 equations that relate these variables are:

1) No Δx: a = (v-v₀) / t

2) No v: Δx = v₀t + ½at²

3) No v₀: Δx = vt - ½at²

4) No t: a = (v²-v₀²) / 2Δx

5) No a: Δx = (v₀ + v)t / 2

For ALL kinematics problems, follow this procedure and you won't go wrong:

1) Write down the variables given in the problem

2) Write down the variable you want to know

3) Find the kinematics equation that relates the variables in steps (1) and (2).

4) Solve that equation for the variable you want to know.

In the equation you gave, this would look something like this (for the sake of argument, say you want to find the final velocity):

-I know: a, v₀, Δx

-I want to know: v

-The equation I should use: (3) a = (v²-v₀²) / 2Δx

Rearrange this to solve for v:

v² - v₀² = 2aΔx

v² = v₀² + 2aΔx

v = ±√(v₀² + 2aΔx)

The "±" means that this equation will give you 2 solutions.  You have to use your intuition to determine which one is the correct solution.