Speed and Velocity

Speed and Velocity

Middle School

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Learning Objectives

• Define and differentiate between speed and velocity.

• Explain the difference between distance and displacement.

• Calculate average speed and average velocity using their respective formulas.

• Interpret motion using distance-time and velocity-time graphs.

Key Vocabulary

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Speed

A measure of how quickly an object covers distance over time, without a specific direction.

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Velocity

The rate an object changes position, including both its speed and its direction of motion.

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Displacement

The shortest distance an object moves from its start to its final position, including direction.

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Distance

The total amount of ground an object has covered during its motion from one point to another.

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Vector Quantity

A physical quantity described by both a magnitude, or size, and a specific direction.

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Scalar Quantity

A physical quantity that is described by a magnitude or numerical value alone, without any direction.

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Distance vs. Displacement

Distance

• ​Distance is the total length of the path an object travels during its motion.

• ​​It is a scalar quantity, which means it only has a size and no direction.

• ​The standard unit for measuring distance is the meter, which is abbreviated as m.

Displacement

• ​Displacement is the straight-line distance and direction from a start point to an end point.

• ​​It is a vector quantity, meaning it has both a size and a specific direction.

• ​If an object returns to its start, the displacement is zero, no matter the distance.

Multiple Choice

A student walks 5 meters east, then turns around and walks 3 meters west. What is the total distance they traveled and their final displacement?

• Distance: 2 meters, Displacement: 2 meters east

• Distance: 8 meters, Displacement: 2 meters east

• Distance: 5 meters, Displacement: 3 meters west

• Distance: 8 meters, Displacement: 8 meters east

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Average Speed vs. Average Velocity

Average Speed

Average Velocity

Multiple Choice

A bus travels a total distance of 300 km over 5 hours on its route. Which statement correctly describes its average speed?

• The average speed is 60 km/h.

• The average velocity is 60 km/h.

• The average speed is 60 km/h east.

• The displacement is 300 km.

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Instantaneous Speed and Velocity

Instantaneous Speed

• Motion can be described at a single moment, which is called instantaneous motion.

• Instantaneous speed is the exact speed of an object at one specific point in time.

• A car's speedometer is a great example, showing the car's speed at that very moment.

Instantaneous Velocity

• Instantaneous velocity is the speed and the direction of an object at a specific instant.

• An object’s velocity can change even if its speed remains constant throughout its movement.

• A car driving in a circle has a constantly changing velocity because its direction changes.

Multiple Choice

Why does a car traveling at a constant speed of 50 mph around a circular track have a changing velocity?

• Because the speedometer is inaccurate on turns.

• Because its speed is not truly constant.

• Because its direction of motion is constantly changing.

• Because its displacement after one lap is not zero.

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Graphs of Motion

Distance vs. Time Graph

• The slope of the line on this graph represents the object's speed.

• A straight line indicates the object is moving at a constant speed.

• A horizontal line means the object is not moving and is at rest.

Velocity vs. Time Graph

• The slope of the line on this graph represents the object’s acceleration.

• A straight line on the graph indicates that the object has constant acceleration.

• The area under the curve represents the object's total change in displacement.

Multiple Choice

On a distance vs. time graph, what does a horizontal, flat line indicate about an object's motion?

• The object is accelerating.

• The object is at rest (speed is zero).

• The object is moving at a constant speed.

• The object is moving in the opposite direction.

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Common Misconceptions: Speed and Velocity

Misconception	Correction
Speed and velocity are the same thing.	Velocity includes direction, but speed does not.
Zero average velocity means an object is at rest.	It can mean the object returned to its starting point.
Constant speed means constant velocity.	Velocity changes if direction changes, even with constant speed.
Average speed is the same as average velocity's magnitude.	Average speed uses total distance, not displacement.

Multiple Choice

A cyclist travels 30 km north and then 40 km east in a total of 2 hours. What is the difference between the cyclist's average speed and the magnitude of their average velocity?

• 50 km/h

• 25 km/h

• 10 km/h

• 35 km/h

Multiple Choice

Why is it possible for a race car to complete a 500-mile race on a circular track and have an average velocity of 0 mph?

• This is not possible; the average velocity must be high.

• Because the race car's final position is the same as its starting position.

• Because the car's instantaneous speed was zero at the end.

• Because the total time taken was exactly one hour.

Multiple Choice

A velocity-time graph for a moving object is a straight line sloping upwards, starting from the origin (0,0). What can you conclude about the object's motion?

• The object started with some velocity and is decelerating.

• The object is at rest.

• The object started from rest and is moving with constant acceleration.

• The object is moving at a constant velocity.

Multiple Choice

A drone flies 5 km north, then 5 km east, and finally 5 km south in 30 minutes. If it then returns to its starting point by flying 5 km west, what is the impact on its overall average speed and average velocity for the entire trip?

• The average speed would remain the same, but the average velocity would change.

• The average speed would increase, and the average velocity would become zero.

• Both average speed and average velocity would become zero.

• The average speed would decrease, and the average velocity would increase.

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Summary

• Speed is how fast an object moves, while velocity includes its direction.

• Distance is the total path covered; displacement is the straight path from start to end.

• An object's velocity changes if its speed, direction, or both change.

• On a distance-time graph, the slope of the line equals the speed.

• On a velocity-time graph, the slope of the line equals the acceleration.

• A round trip has an average velocity of zero because the displacement is zero.

Poll

On a scale of 1-4, how confident are you about calculating speed and velocity?

• 1

• 2

• 3

• 4