# Speed and Velocity

## Introduction

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:

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:

### 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*

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Date of last modification: 2024