Measurement of Time and Motion · Lesson 4 of 6
Finding Distance, Time, and Average Speed
“Use the speed relationship in three directions and interpret what a whole-journey speed means.”
• Find distance when speed and time are known. • Find travel time when distance and speed are known. • Keep units consistent in multi-step calculations. • Explain why total distance divided by total time is average speed. • Compare journeys using calculated average speeds rather than a single moment of motion.
One Relationship, Three Questions
Speed connects the distance travelled with the time taken. If a bus maintains 50 km/h, it covers 50 km in one hour and 100 km in two hours. Multiplying speed by time therefore gives distance. Reversing the question, dividing distance by speed gives the time needed at that speed.
These relationships come from the definition speed = distance ÷ time. Multiplying both sides by time gives distance = speed × time; dividing distance by speed gives time. They describe a journey at the stated constant speed, or a whole journey when the stated speed is its average.
Find a Distance
Decide what distance one time unit represents before multiplying. This makes the arithmetic easier to check: 50 km/h for two hours ought to be twice 50 km, not half of it.
Problem
A bus travels at 50 km/h for 2 h. How far does it travel?
- 1.The speed means 50 km are covered in each hour at this pace.
- 2.Multiply: distance = 50 km/h × 2 h. The hour units cancel.
- 3.The distance is 100 km.
Problem
A student walks at 2 m/s for 3 min. How far does the student travel at this steady speed?
- 1.Convert 3 min to 3 × 60 s = 180 s.
- 2.Multiply speed by time: 2 m/s × 180 s.
- 3.The student travels 360 m. Multiplying by 3 without converting minutes would give the wrong result.
Find the Time
The same relationship can answer when an object will arrive. Divide the total distance by the distance covered in one unit of time. The unit in the answer must match the time unit built into the speed.
Problem
A train covers 360 km at 90 km/h. How much time does it take?
- 1.Write time = distance ÷ speed.
- 2.Compute 360 km ÷ 90 km/h = 4 h.
- 3.Check: in four hours at 90 km each hour, the train covers 360 km.
Problem
A toy moves 150 m at 5 m/s. How long does it take?
- 1.The distance is in metres and the speed is in metres per second, so the answer will be in seconds.
- 2.Calculate 150 m ÷ 5 m/s = 30 s.
- 3.Check by multiplying 5 m/s × 30 s = 150 m.
What a Whole-Journey Speed Tells Us
A bus may stop, accelerate, and slow down. Dividing its total distance by its total elapsed time still gives a useful single number: its average speed for the whole journey. It does not claim that the bus moved at that speed at every moment. A speedometer can show a momentary speed that is different from this whole-journey value.
Problem
A car covers 60 km in the first hour and 40 km in the next hour. Find its average speed for the full trip.
- 1.Add distances: 60 km + 40 km = 100 km.
- 2.Add times: 1 h + 1 h = 2 h. Divide totals: 100 km ÷ 2 h.
- 3.The average speed is 50 km/h, even though neither hour was travelled at 50 km/h throughout.
If two sections take different amounts of time, the arithmetic mean of their speeds is generally not the journey’s average speed. Add the section distances and the section times, then divide the totals.
Problem
A cyclist rides 10 km in 1 h, then 20 km in 0.5 h. What is the average speed?
- 1.Add distances: 10 km + 20 km = 30 km.
- 2.Add times: 1 h + 0.5 h = 1.5 h.
- 3.Average speed = 30 km ÷ 1.5 h = 20 km/h. The section speeds were 10 km/h and 40 km/h; their simple arithmetic mean, 25 km/h, would be wrong here.
Collect the winning times for 100 m, 200 m, and 400 m races. Divide each race distance by its own recorded time and use the same speed unit for every comparison. Treat the result as an average over that race distance.
Quiz
A vehicle travels at 40 km/h for 3 h. What distance does it cover?
How long does a train take to cover 240 km at 80 km/h?
A toy moves at 2 m/s for 2 min. What distance does it cover?
Why can average speed differ from the reading of a speedometer at one moment?
A vehicle covers 30 km in 1 h and 90 km in 3 h. What is the average speed for the full trip?
Which values are needed to find whole-journey average speed?
Practice Problems
- A bus maintains 55 km/h for 2 h. Find its distance and explain the unit cancellation.
- A train travels 150 km at 75 km/h. Find its travel time.
- A walker moves at 1.5 m/s for 4 min. Calculate the distance in metres.
- A car travels 60 km in one hour, 70 km in the next, and 50 km in the third. Find the whole-journey average speed.
- Two journeys have the same distance but different total times. Explain which has a larger average speed.
- A vehicle travels 2 km in 200 s. Express its average speed in m/s and explain why a speedometer might show other values along the way.
Key Takeaways
• Distance equals speed multiplied by time; time equals distance divided by speed. • Convert units before calculating and check the answer by reversing the operation. • Average speed uses the total distance and the total elapsed time. • A whole-journey average does not describe every moment of a journey.