# B Adding Velocity and Acceleration

1. Aug 23, 2016

### Phys_Boi

So if a particle is at (0,0) and has a velocity of <-3,0> and an acceleration of <-2,-4> then we would add them to get the new position...

With a time interval of one second (t=1) then due to velocity:
Δx = -3(1) = -3
Δy = 0(1) = 0

then due to acceleration:
Δx = ½ (-2) (1)^2 = ½ (-2) = -1
Δy = ½ (-4) (1)^2 = ½ (-4) = -2

so we can add these displacements to get a new position of (-4, -2)

So my question is: after we arrive at this point and the acceleration has affected the velocity (and assuming the acceleration continues) is there another velocity vector? Or is there just the acceleration? Basically, do you only use the velocity once and forget it? Or does it still exist, and if so, how do you calculate it?

Thank you for any help!

2. Aug 23, 2016

### Michael Quinlivan

For a constant acceleration, you can calculate the velocity of an object with the formula $$v = v_0 + at$$ where $v_0$ is the initial velocity before you start timing, and $v$ is the new velocity after a time $t$, if the object experiences a constant acceleration $a$. Using this formula you should be able to calculate the new velocity of the particle after one second

3. Aug 23, 2016

### Phys_Boi

So I'm using gravitational acceleration..
a = GM/r2

how would I calculate the velocity for this changing acceleration?

4. Aug 23, 2016

### Michael Quinlivan

If you need to calculate the velocity of a falling body, where the acceleration due to gravity varies, have a look at this link

https://en.wikipedia.org/wiki/Equations_for_a_falling_body

Note that these formulae don't take into account factors like air resistance, etc.

5. Aug 23, 2016

### Phys_Boi

Thank you sir