Describing Motion Around Us · Lesson 3 of 10
Average speed and average velocity
“Speed counts every step; velocity also asks which way you ended up.”
• Calculate average speed from total distance and total time. • Calculate average velocity from displacement and time. • Distinguish uniform from non-uniform straight-line motion. • Explain rate of change using velocity. • Convert between common speed units. • Identify when average speed equals average-velocity magnitude.
Two students may start and finish a walk at the same places and take the same time, yet one may wander along a longer route. Their displacements and average velocities are equal, but their distances and average speeds are not. The distinction comes from the quantity used in the numerator.
Average speed is the total distance travelled divided by the time interval during which that distance is covered.
An object is in uniform straight-line motion when it travels equal distances in equal intervals of time for all suitable equal intervals.
An object is in non-uniform straight-line motion when it travels unequal distances in equal intervals of time.
During uniform motion, speed remains constant. In non-uniform motion, speed may increase, decrease or do both during different parts of the journey. A single average speed describes the whole interval but does not reveal every change within it.
India’s Scientific Contributions
The relationship between distance, time and speed has been studied for centuries. A historical problem describes two postmen walking toward each other from a separation of 210 yojanas. One covers 9 yojanas per day and the other 5 yojanas per day. Their combined closing speed is 14 yojanas per day.
Problem
How long will two postmen separated by 210 yojanas take to meet if they cover 9 and 5 yojanas per day?
- 1.Because they move toward each other, add their daily distances: (9+5=14) yojanas per day.
- 2.Together they must close the full separation of 210 yojanas.
- 3.Time = distance ÷ combined speed.
- 4.Time = (210÷14=15) days.
- 5.Check: the first covers (9×15=135) yojanas and the second (5×15=75) yojanas; (135+75=210).
Average velocity is the displacement divided by the time interval in which that displacement occurs.
Rate of change is the change in one quantity divided by the corresponding change in time.
Average velocity is the average rate of change of position. It requires direction because displacement has direction. For straight-line motion, the sign of displacement also gives the sign of average velocity.
| Unit | Meaning | Conversion |
|---|---|---|
| m s⁻¹ | metres travelled each second | Base unit used in calculations |
| km h⁻¹ | kilometres travelled each hour | Multiply by 5/18 to obtain m s⁻¹ |
| m s⁻¹ to km h⁻¹ | Reverse conversion | Multiply by 18/5 |
Problem
A swimmer covers 25 m to the other end and 25 m back in 50 s. Find average speed and average velocity.
- 1.Total distance = (25+25=50 m).
- 2.Average speed = (50÷50=1 m s⁻¹).
- 3.The swimmer finishes at the starting position, so displacement = 0.
- 4.Average velocity = (0÷50=0 m s⁻¹).
- 5.The different answers arise because distance and displacement are different.
Pause and Ponder
Problem
A family drives 200 km north in 3 h and 200 km south in 2 h. Find average speed and average velocity.
- 1.Total distance = (200+200=400 km).
- 2.Total time = (3+2=5 h).
- 3.Average speed = (400÷5=80 km h⁻¹).
- 4.Final position equals initial position, so displacement = 0.
- 5.Average velocity = (0÷5=0 km h⁻¹).
Threads of Curiosity
A speedometer reading is nearly the magnitude of velocity at that instant. It does not by itself provide the direction. The direction in which the tyres and vehicle are moving completes the description of velocity.
Ready to Go Beyond
Velocity at a particular instant is called instantaneous velocity. It can be imagined by calculating average velocity over intervals surrounding the instant and making those intervals progressively smaller. The detailed mathematical process is studied later; here, “velocity” will usually refer to the value at an instant when discussing graphs and equations.
For a multi-part journey, first add all distances and all time intervals. The arithmetic mean of two speeds is correct only in special cases.
Quiz
Which description best matches Average Speed?
Which description best matches Uniform Motion in a Straight Line?
Which term matches this description: Average speed is the total distance travelled divided by the time interval during which that distance is covered.
Which term matches this description: An object is in uniform straight-line motion when it travels equal distances in equal intervals of time for all suitable equal intervals.
Which statement is a key takeaway from this lesson?
Practice Problems
- A cyclist covers 300 m in 20 s and 200 m in 10 s. Find average speed.
- A runner completes one 400 m lap in 80 s. Find average speed and average velocity.
- Convert 72 km h⁻¹ to m s⁻¹.
- State the condition under which average speed equals average-velocity magnitude.
Key Takeaways
• Average speed uses total distance. • Average velocity uses displacement and direction. • Uniform motion covers equal distances in equal time intervals. • A round trip has zero average velocity but may have non-zero average speed. • Rates must be calculated using consistent units.