Let's not forget our joke.

Our definition of velocity.

Average velocity, instantaneous velocity.

Changing velocity but not speed.

Acceleration.

ILD1: Different acceleration and velocity graphs.

Using acceleration to determine velocity and position.

Definition:

average velocity is the change in position (Dp here) over the change in time, Dt.

Aside: To get to Crow, Oregon, then, one could tell another to travel east at -0.09km/hour

(since its a negative speed, that's traveling west)

Do this while travelling north at -0.063km/hr (same idea, your really traveling south).

Do both at the same time, for an hour, and you will arrive in Crow (we'll ignore the elevation gain for now).

So velocity is a speed and direction, which can be represented by an arrow (sometimes called a "vector"). The length of the arrow is the speed, a longer arrow means greater speed. The direction of the arrow is... well duh!...the direction. Any arrow can be represented by components in certain agreed-upon (usually perpendicular) directions, say north, east and up.

Instantaneous velocity and average velocity:

The term instantaneous velocity refers to velocity at an instant.

• Your car's speedometer appears to tell you the car's speed at each instant.
• This is an interesting idea, as the above formula suggests you need to know TWO positions and TWO DIFFERENT times to know velocity.

Average velocity is the speed averaged over the time interval, along with the direction.

• There are many different ways to achieve the same average velocity.
• Average velocity is determined simply by the time it takes to go between to positions.
• The direction from the first position to the second is the direction of velocity.

...and remember, velocity is relative.

Changing velocity but not speed.

Well... can we? If so, how? Can we change speed without changing velocity?

Acceleration.

What is this thing called acceleration? We define it to be related to velocity vs. time graphs.

Definition: average acceleration is the change in velocity over the time elapsed.

Acceleration tells us about change in velocity. If our initial velocity is zero, then acceleration can tell us our velocity after some time using the simple relationship:

How Fast

Say you just ran off the end of a cliff, and plan to descend for 5 seconds before hitting the valley floor with a little puff.

In the several moments while you wait to fall (just kidding!) you estimate how fast will you will traveling when you hit:

In fact, Wile E Coyote will be travelling 10 m/s after 1 second of fall, 20 m/s after 2, 30 m/s after 3 seconds, and so on.

{note: we are ignoring the force of air resistance, which will oppose his fall and, eventually, equal the force of gravity exerted downwards on Wile (what does that tell you about the air resistance force's relationship to speed?). When this happens, Wile has reached terminal velocity and won't speed up any more (lucky guy!)}

How Far

You ran off the end of a cliff, but don't know how far you will fall. How far will you travel (ever downward!) after 5 seconds of falling?

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