 # Motion in One Dimension. How physicists describe motion:  Displacement, not distance  Position-time graph  Velocity, not speed  Slope: steeper means.

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Motion in One Dimension

How physicists describe motion:  Displacement, not distance  Position-time graph  Velocity, not speed  Slope: steeper means faster

Distance: The separation between two points. A scalar quantity.

Displacement: Change in position. A vector quantity.

In one dimension, there are only two possible directions. For example: Right or left Up or downNortheast or Southwest In physics, we use Positive or negative

Meet Mr. Morris Shun (His friends call him Moe.)

0 m1 m-1 m Watch Moe go … What was his displacement? One meter.

0 m1 m-1 m Check this out … What was Moe’s displacement? Negative two meters.

0 m1 m-1 m Gettin’ jiggy now … What was Moe’s displacement? Zero meters.

Let’s graph it! 0 m1 m -1 m position (m) 0 1 time (s)

Velocity: Displacement per unit of time. A vector quantity. In one dimension, velocity will be either positive or negative. v = ΔxΔx ΔtΔt (The Greek letter Δ – delta – means “change in”)

time (s) 0 position (m) 1 1 23 What was Moe’s average velocity for the first second? Rise = 1 m Run = 1 s Velocity = Displacement Time = Rise Run = 1 m s 1 m 1 s =

In a position-time graph, the slope of the line gives us the object’s velocity. Slope = rise/run. In other words, the steeper the line, the faster the object is moving

The sign of the slope gives you the direction of the object. Lines that go from lower left to upper right have positive slope and positive velocity. The object is moving forward. Lines that go from upper left to lower right have negative slope and negative velocity. The object is moving backward.

What is the velocity if the line is horizontal? Zero. The rise is zero because the displacement is zero. Slope = rise/run, and zero divided by anything is zero. The object is not moving.

What do you have if the line is vertical? A mistake. The run is zero. Slope = rise/run, and you can’t divide by zero. A vertical line would mean the object was at many different positions at the same time.

time (s) 0 Position (m) 1 1 23 What was Moe’s average velocity for the last two seconds? Rise = − 2 m Run = 2 s Velocity = Displacement Time = Rise Run = = - 2 m 2 s m s

Time (s) 0 Displacement (m) 1 1 23 What was Moe’s average velocity over all three seconds? Rise = − 1 m Run = 3 s Velocity = Displacement Time = Rise Run = = - 1 m 3 s - 0.3 m s

 The slope of a line on a position-time graph equals the velocity of the object in motion. Moe knows …  Displacement is change in position. It’s a vector quantity.  Velocity is displacement per unit of time. It’s also a vector quantity.

Get ready to say goodbye to Moe!

Scalar: A quantity that has magnitude but no direction.

Vector: a quantity with magnitude and direction.

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