GCSE · Physics · Edexcel · Spec 1PH0

Speed equation

A cyclist averages 4 m/s on her 1200 m ride to school. Yet no stretch of the ride was at 4 m/s, and she even stopped at a red light.

A 5-minute ride to school: fast, stopped, then slow

time (s): 150. distance travelled (m): 960. Average speed for the whole ride: 4 m/s

Drag the dot along the ride. The numbers are (time in s, distance in m). Find the fast stretch, the stop at the lights and the slow push up the hill.

The straight line: an imaginary rider going at a steady 4 m/s the whole way. It covers the same 1200 m in the same 300 s, and that is all an average speed tells you. The real rider races ahead of it on the flat road, waits at the lights, crawls up the hill, and only meets the steady rider at the finish.

Watch out: The flat part is the red light. The clock keeps running but the distance stays stuck at 960 m. Those 60 seconds still count in the total time. She stood completely still, yet the trip as a whole still has an average speed of 4 m/s.

The speed triangle

Tap the quantity you want to find. The triangle shows you the formula.

Cover distance travelled, average speed or time to reveal its rearranged formula, then plug in numbers to solve.

Your turn: fill in the missing steps

A runner jogs 600 m in 200 s, then sprints 400 m in 50 s. (a) What is her average speed for the whole run? (b) At that same average speed, how long would a 1400 m run take? Pick the right line for each gap.

(a) Average speed for the whole run = total distance ÷ total time, so find both totals first.
Total distance = 600 m + 400 m = 1000 m. Total time = 200 s + 50 s = 250 s.
missing step

Which line is step 3?

Average speed = 1000 m ÷ 200 sAverage speed = 1000 m ÷ 250 sAverage speed = 250 s ÷ 1000 m

Out fast, back slow: what's the average?

Maya cycles 900 m to the park at a steady 6 m/s. She cycles the same 900 m home, uphill, at a steady 2 m/s.

What was Maya's average speed for the round trip? Pick the answer closest to what you think, then say how sure you are.

4 m/s. It's halfway between 6 m/s and 2 m/s.3 m/s. That's 1800 m in total, divided by 600 s in total.You can't tell without knowing her speed at every moment of the trip.

How sure are you?

I'm sureI think soI'm guessing

4 m/s. It's halfway between 6 m/s and 2 m/s.

This is a common misconception

Tempting, but that only works if she spent the same TIME at each speed, and she didn't. Going out took 900 ÷ 6 = 150 s. Coming back took 900 ÷ 2 = 450 s, three times as long. She spent most of the trip going slowly, so the average gets dragged down towards 2 m/s. Total distance ÷ total time = 1800 m ÷ 600 s = 3 m/s.

3 m/s. That's 1800 m in total, divided by 600 s in total.

This matches the evidence

Exactly right. Out: 900 ÷ 6 = 150 s. Back: 900 ÷ 2 = 450 s. Totals: 1800 m and 600 s, so the average speed is 1800 ÷ 600 = 3 m/s. Notice it's closer to 2 m/s than to 6 m/s, because most of her time was spent on the slow, uphill part.

You can't tell without knowing her speed at every moment of the trip.

This is a common misconception

You don't need every moment, and that's the whole point of an average speed. It only needs two totals: how far altogether and how long altogether. Here each leg's time comes from distance ÷ speed: 150 s and 450 s. So it's 1800 m ÷ 600 s = 3 m/s.

Don't average the speeds. Add up the distances, add up the times, then divide.

Spot the slip: find the line that goes wrong

A bus travels 4.8 km in 8 minutes. Calculate its average speed in m/s. Tap the line where this answer first goes wrong.

A student's answer — which line goes wrong?

average speed = distance ÷ time
distance = 4.8 km = 4.8 × 1000 = 4800 m
average speed = 4800 ÷ 8
average speed = 600
Answer: 600 m/s

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

One number for a whole journey, and why the object was hardly ever doing that speed.

What you need to know

Speed is the distance travelled per unit time: 5 m/s means 5 metres every second.
Average speed = total distance travelled ÷ total time taken.
Rearranged: distance = average speed × time, and time = distance ÷ average speed.
For m/s, use metres and seconds: 1 km = 1000 m and 1 minute = 60 s.
An object can be faster or slower than its average speed at different moments.

The big picture

Speed is how much distance something covers each second. For a whole journey, average speed = total distance ÷ total time, and that includes stops and slow bits. The same relationship rearranges to give distance (average speed × time) or time (distance ÷ average speed). Put distances in metres and times in seconds before you substitute, and the speed comes out in m/s. An average speed is one number for the whole trip: at any moment the object may be going faster or slower than it.

Key points

1Average speed squeezes a whole journey into one number: total distance ÷ total time.

2Stops count. Standing still adds to the total time but not to the distance, so it lowers the average speed.

3Average speed is not simply the mean of the different speeds. The longer you spend going slowly, the closer the average gets to the slow speed.

4If an object was slower than its average speed at some moments, it must have been faster than its average speed at others.

5Distance = average speed × time: 4 m every second for 300 s is 1200 m. To find speed or time, divide the distance by the other one.

6Convert before you substitute: kilometres × 1000 for metres, minutes × 60 for seconds. Skip it and the answer comes out in the wrong unit.

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Worked example

Problem

A train travels at an average speed of 25 m/s for 4 minutes. How far does it travel? Give your answer in km.

⚠ Watch out

Putting kilometres or minutes straight into average speed = distance ÷ time. The number that comes out is then in km per minute or metres per minute, not m/s. Convert first: kilometres × 1000 and minutes × 60.

🧠

Memory hook

Total over total, and the stops still count. And for the triangle: distance sits on top because speed × time builds it.

✓

Check yourself

A car's average speed over a 30 km journey is 20 m/s. How long did the journey take, in seconds? And was the car doing 20 m/s the whole way?

Flashcards

(11)

What is speed?

The distance an object travels per unit time. A speed of 3 m/s means 3 metres every second.

How do you find the average speed for a whole journey?

Total distance travelled ÷ total time taken.

What units give a speed in m/s?

Distance in metres (m) and time in seconds (s).

Why is distance = speed × time?

Speed is metres per second, so multiplying by the number of seconds adds up all the metres. 4 m every second for 300 s is 1200 m.

You know the distance and the average speed. How do you find the time?

time = distance ÷ average speed.

How do you turn kilometres into metres?

Multiply by 1000 (1 km = 1000 m).

How do you turn minutes into seconds?

Multiply by 60 (1 minute = 60 s).

Distance in metres, time in minutes: what goes wrong if you divide straight away?

You get metres per MINUTE, not metres per second. Convert the minutes to seconds first.

Does an average speed of 4 m/s mean the object moved at 4 m/s all the time?

Not necessarily. At different moments it can be faster or slower than 4 m/s. The average is one number for the whole journey.

A journey includes a stop. Does the stopped time go into the average speed?

Yes. It adds to the total time but not the distance, so it pulls the average speed down.

Why isn't the average speed just the mean of the speeds?

The object usually spends different amounts of time at each speed, and time spent going slowly drags the average down. The two only agree if equal times are spent at each speed, so always use total distance ÷ total time.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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A 5-minute ride to school: fast, stopped, then slow

Your turn: fill in the missing steps

Out fast, back slow: what's the average?

Spot the slip: find the line that goes wrong

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