Describing Motion: Quick Revision

A brief note on Describing Motion. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Reference point. Rest and motion are always compared with something. A passenger is at rest compared to the seat and moving compared to the road.
• Distance is the length of the whole path. Displacement is the straight line from start to end, with a direction.
• Speed $=$ distance $\div$ time. Velocity $=$ displacement $\div$ time.
• Average speed $=$ total distance $\div$ total time, counting the stops.
• $1\ \text{km/h} = \tfrac{5}{18}\ \text{m/s}$.

The facts at a glance

A worked example

A bus on a straight road goes $9\ \text{km}$ north in $15$ minutes, $3\ \text{km}$ back south in $6$ minutes, then $6\ \text{km}$ north in $9$ minutes. Find its average speed and average velocity.

1. Distance. $9\ \text{km} + 3\ \text{km} + 6\ \text{km} = 18\ \text{km}$. Displacement. $9\ \text{km} - 3\ \text{km} + 6\ \text{km} = 12\ \text{km}$ north.
2. Time. $30$ minutes, or $0.5\ \text{h}$.
3. Averages. Speed $\dfrac{18\ \text{km}}{0.5\ \text{h}} = 36\ \text{km/h}$; velocity $\dfrac{12\ \text{km}}{0.5\ \text{h}} = 24\ \text{km/h}$ north.

Practice with new numbers

A program to try

The program works out the bus trip.

Mistakes to avoid

• Forgetting the reference point. Say what you compare with.
• Adding opposite legs for displacement. On a straight road, subtract them.
• Averaging the speeds. Divide the total distance by the total time instead.
• Mixing units. Change km/h to m/s before you use seconds.
• Leaving out the stops. The clock keeps running while you wait.

Check yourself

1. What is $36\ \text{km/h}$ in m/s?

2. A boy walks $8\ \text{m}$ east and then $6\ \text{m}$ north. What is his displacement?

3. A runner finishes one lap where she started. What is her average velocity?

4. You sit in a moving bus. Are you at rest or moving?

5. A car goes $100\ \text{km}$ in $2.5$ hours. What is its average speed?