1 of 13

Speed & Velocity

Unit 2: One-Dimensional Motion

2 of 13

Scalar vs Vector: What are the differences?

Scalar:

Vector:

  • Does NOT depend on direction
  • Fully described by a number
  • How far the object has moved during its motion
  • Direction aware
  • Describes how out of place the object is at the end of the motion

3 of 13

Speed:

Velocity:

  • Scalar quantity
  • Speed refers to how fast an object is moving
  • Can also be considered the rate at which an object covers a distance
  • Vector quantity
  • Velocity refers to the speed of an object in a given direction

4 of 13

Velocity Example

You take one step forward, one step back, repeat

What is your velocity?

Velocity = ZERO

Why?

You’re always returning to the starting position

Your displacement is zero

5 of 13

Velocity = Vector

  • Velocity is direction aware
  • You must keep track of the direction of the object when determining velocity

Example: 55 mph

55 mph, east

≠ velocity

= velocity

6 of 13

Determining the Direction of the Velocity

It’s easy!

  • The direction of the velocity = the direction the object is moving
  • It doesn’t matter if the object is speeding up or slowing down

7 of 13

Calculating Average Speed

Average Speed =

total distance

total time

8 of 13

Calculating Average Velocity

Average Velocity =

Δ position

time

displacement

time

=

Δ = “delta” = “the change in”

9 of 13

Average Speed vs Instantaneous Speed

  • Average speed: found by a distance-time ratio
  • Instantaneous speed: the speed at any given instant
  • Example: the speedometer in a car
    • You may AVERAGE 55 mph on your drive to school
    • But your INSTANTANEOUS speed is the speed your speedometer reads at any given point in time

​

10 of 13

Example #1:

You walk:

  • 4 m, East
  • 2 m, South
  • 4 m, West
  • 2 m, North
  • The walk lasts for 24 s

4 m

4 m

2 m

2 m

What is your average speed? Your average velocity?

11 of 13

Example #1:

Average speed:

total distance ÷ total time

12 m ÷ 24 s =

4 m

4 m

2 m

2 m

Average velocity:

displacement ÷ total time

0 m ÷ 24 s =

0.5 m/s

0 m/s

12 of 13

Example #2: A cross-country skier

What is the skier’s average speed from A to D?

What is the skier’s average velocity from A to D?

13 of 13

Example #2: A cross-country skier

Average speed:

total distance ÷ total time

420m ÷ 3 min =

Average velocity:

displacement ÷ total time

140 m ÷ 3 min =

140 m/min

46.7 m/min →