Introdction to Speed and Velocity

Distance, Speed, and Velocity

Just as distance and displacement have distinctly different meanings, so do speed and velocity.
Speed is a scalar quantity that refers to "how fast an object is moving."
Speed can be thought of as the rate at which an object covers distance and its formula is: v = d/t where d is the distance and t is time.
Example: Assume that Mike took him 2 hours minutes to walk 6 miles. What is his speed in miles per hour (mph) during this exercise?
Answer: v = 6 / 2 = 3 mph.

Exercise: Unit Conversion

Exercise 1:

Question: Convert 80 kilometers per hour to miles per hour. Solution:
1 km = 0.6214 miles; 1 mile = 1.609 km
80 km/h × 0.6214 = 49.71 mph

Average Speed

Average Speed = Distance Traveled / Time of Travel

Exercise 2:

Question: Calculate the average speed of a Taxi driver who started a trip from point A to D passing by B and C with speed mentioned in the figure below:
Track1

Track1

Check your answers here: Solution: Average speed exercise

Question: Convert your answer to km/h.
Answer: 47.94 kmh

Exercise

Adam drove for 4 hours at a rate of 70 miles per hour and for 3 hours at 55 miles per hour.
Question: What was his average speed for the entire trip?
Check your answers here: Solution: Average Speed Exercise

Velocity

Velocity is a vector quantity that refers to "the rate at which an object changes its position."
As depicted below the velocity requires direction:

Velocity

Average Velocity

Average Velocity = Displacement / Time = ΔPosition / Δt = Δd / Δt
Note the difference between distance and displacement.

Displacement is "how far out of place an object is" it is the object's overall change in position.
The speed at any instant is called instantaneous speed.
The speedometer in the car gives instantaneous speed.

Exercise

Let's assume that Joe while jogging, during the first two hours of his exercise,
he ran a distance from work started from 0 to 8 miles, while the time in hours went from 0 to 2.
Question 1: Calculate his average velocity.

Question 2:
During the next three hours, the distance from his work went from 8 to 23 while the time went from 1 to 4.
Calculate his average velocity.

Check both answers here: Average Velocity Exercise

Frequently Asked Questions

Q: What is the difference between speed and velocity?

A: Speed is a scalar quantity that measures how fast an object is moving, with no reference to direction.
Velocity is a vector quantity that measures the rate of change of position and includes direction. For example, "50 mph" is a speed, while "50 mph heading north" is a velocity.

Q: What is the formula for speed?

A: Speed = Distance ÷ Time, often written as v = d/t. For example, if an object travels 6 miles in 2 hours, its speed is 3 mph.

Q: What is average speed?

A: Average speed is the total distance travelled divided by the total time taken.
It gives an overall rate of movement across an entire journey, not just one segment.

Q: What is instantaneous speed?

A: Instantaneous speed is the speed of an object at a specific moment in time.
A car's speedometer displays instantaneous speed.

Q: What is the difference between displacement and distance?

A: Distance is the total length of the path travelled, regardless of direction.
Displacement is the straight-line change in position from start to finish, including direction.
An object could travel a large distance but have zero displacement if it returns to its starting point.

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