Physics of Motion: What is What?

The equations:

df = di + (vi)(t) + (½)(a)(t2) This will answer almost all “how far” questions.

Use this if:

Only 1 velocity is given

You have a distance given (df is rarely 0, but sometimes it is the unknown)

Only 1 velocity is given

You have a distance given (df is rarely 0, but sometimes it is the unknown)

∆d = v(ave)∆t

Use this if:

You only need to find how much something moved in a period of time, not how far it ends up from a point of reference.

You only need to find how much something moved in a period of time, not how far it ends up from a point of reference.

vf = vi + (a)(t) This will answer almost all “how fast” questions.

Use this if:

2 velocities are given

You don’t have distance

2 velocities are given

You don’t have distance

∆v = a∆t

Use this if:

You only need to find how much velocity changed over a period of time, not what its final or initial velocity was/is.

You only need to find how much velocity changed over a period of time, not what its final or initial velocity was/is.

v(ave) = (vi + vf)/2 (See * below)

Use this if:

You need to find the average velocity

You know BOTH vi and vf (you might have to calculate vf!

You need to find the average velocity

You know BOTH vi and vf (you might have to calculate vf!

vf = (vi + ∆v)

Use this if:

You need to find the final velocity AND

You know BOTH vi and how much v changes (e.g. speed increases by 10 m/s)

You need to find the final velocity AND

You know BOTH vi and how much v changes (e.g. speed increases by 10 m/s)

df = (di + ∆d)

Use this if:

You need to find the final distance, total distance, or final position AND

You know BOTH di and how much d changes (e.g. it moves 10 meters)

You need to find the final distance, total distance, or final position AND

You know BOTH di and how much d changes (e.g. it moves 10 meters)

The hints and helps:

It is vi if…

“…traveling at a rate of…”

“…moving at…”

"…has a velocity of…"

"…has a velocity of…"

If it is “at rest” then vi = 0

*and*di is probably 0
The words "begin" and "starts" generally go with the

**initial**values.

If it is “moving at a constant” rate or if it “has a constant velocity” then a = 0

It is possible that something not given (but which is not the thing to be found) should have a value of 0...

*Another v(ave) approach:

*v(ave) = ((vi + at) + vi)/2*

Use this if: You need to find the average velocity You know vi and but you have to calculate vf