Motion in One Dimension Chapter 2 Motion in One Dimension

Motion in One Dimension Leading Question: What is one dimensional motion? Answer: The simplest form of motion i.e. a train moving on a track can only move back and forth

You in motion Try to think of all the ways you’re moving right now Earth is rotating on its axis Earth is revolving around the Sun The solar system is orbiting the Milky Way So….how can we really come up with a simple way to describe an object’s motion?

Frames of Reference A frame of reference: A coordinate system for specifying the precise location of objects in space So what could be a frame of reference for a train? Stations along track Any frame of reference can be chosen as long as you’re consistent

Displacement What is displacement? A change in position

Displacement Eqn Displacement= change in position= final position – initial position Since displacement is relative to the starting position, direction is necessary!

The Sign of displacement indicates direction ! In your book (unless otherwise stated) motion to the right or up is positive and motion to the left or down is negative

Sign Conventions Positive Directions Negative Directions Up Down Right Left North South East West

Displacement isn’t the same as distance traveled Say you went from your friend’s house to the grocery store. What would be your displacement? What is your distance traveled?

The distance traveled would be 6.4 miles. The displacement would be 6.4 miles East (or to the right). You must include direction! Now say you traveled from your friend’s house to the grocery store and then returned to your friend’s house. What is your distance traveled and what is your displacement?

Distance vs Displacement Distance traveled: 6.4 mi + 6.4 mi = 12.8 mi Displacement: 0 mi! Because final position = initial position.

Velocity Average velocity is the change in position divided by change in time. Average velocity can be positive or negative!!

Example During a race, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s displacement in 137 s? Notice that the velocity is positive which means that east is positive. Rearrange the displacement equation: Plug in your values and solve: = (6.02 m/s)(137 s)= 825 m to the east

Velocity is not the same as speed Average Speed = distance traveled time of travel Average Velocity= displacement VELOCITY HAS DIRECTION. SPEED DOES NOT.

What information does the graph show? How would you calculate the slope of the line? Slope = rise = change in vertical coordinates run change in horizontal coordinates Slope = Δx = AVERAGE VELOCITY!!! Δt So the moral of the story is….THE SLOPE OF AN OBJECT’S POSITION VS TIME GRAPH = THE AVERAGE VELOCITY OF THE OBJECT

Instantaneous Velocity Instantaneous velocity of an object is the velocity at some instant…so it can be different than average velocity To calculate instantaneous velocity you need to measure the slope of a line that is tangent to the graph at that instant.