KS3 · Physics

Measuring speed accurately

A trolley crosses the finish line at 2 m/s. So its speed was 2 m/s, right? Not quite, and that's the whole lesson.

Timing a trolley down a ramp

Step through the stages. Before you read each 'why', try to guess it.

Count down: 3, 2, 1, goCount down out loud and start the stopwatch on 'go'. Counting down helps you start the stopwatch at the right moment, instead of guessing when to press.
Eyes in line with the finishPut your eyes in line with the finish line so you can stop the stopwatch at the right moment. Watching from the side of the line gives a timing error.
Time between the linesThe stopwatch runs only while the trolley travels from the start line to the finish line. That time, together with your 1 m, is one measurement.
Take the mean timeAdd your times together and divide by how many there are. That turns several timings into one time you can use.

Your turn to do the sums

From timings to speed

A trolley rolls 1 m down a ramp and is timed three times: 1.34 s, 1.31 s and 1.37 s. Find the mean time and the average speed. Then find the time between two video stills.

Three repeat times for the 1 m run: 1.34 s, 1.31 s, 1.37 s.
Plan: one mean time first, then average speed = distance ÷ time.
missing step

Which line is step 3?

Add the three times: 1.34 + 1.31 + 1.37 = 4.02 sPick the biggest time, 1.37 s, to be safeSubtract smallest from largest: 1.37 − 1.31 = 0.06 s

Spot the slip

Where does this answer go wrong?

A trolley takes 0.25 s to travel 10 cm. Find its speed in m/s.

A student's working — which line goes wrong?

Speed = distance ÷ time
Distance = 10, time = 0.25 s
Speed = 10 ÷ 0.25 = 40
Speed = 40 m/s

Predict, then check

Pick before you reveal. Commit to one answer.

A trolley starts from rest and crosses the finish line at 2 m/s. What is its average speed on the way down?

Two different questions

Average speedvsInstantaneous speed

Cover the right-hand column and predict each row first.

Focus

What it tells you

Average speed

The total distance travelled divided by the total time taken

Instantaneous speed

The speed at one particular moment

The insight

One number for the whole trip, against a snapshot of a single moment.

During a journey

Average speed

One value for the whole distance

Instantaneous speed

Changes as the object speeds up and slows down

Compared with each other

Average speed

Not always the same as the instantaneous speed

Instantaneous speed

Can be higher or lower than the average speed

On a car dashboard

Average speed

The speedometer does not show this

Instantaneous speed

The speedometer shows this

How you measure it

Average speed

Time the whole distance, then distance ÷ time

Instantaneous speed

Time a very short distance with an electronic timer, e.g. a few centimetres near the end of the ramp

A sprinter's top speed

Average speed

Not found by timing the whole race

Instantaneous speed

Poles 10 m apart, a run-up so they reach top speed, timed between the poles, then repeat for an average time

What do you think?

Timing errors

A student times a trolley between two lines by hand, using a stopwatch, several times.

Which is closest to what you think right now?

If I repeat the timing enough times, every error disappears.Every reading has to go into the mean, even the odd one that is miles off.My reaction time always makes the time too long.Timing by hand gives errors that vary from test to test, so I should repeat the timing and use the mean.

How sure are you?

I'm sureI think soI'm guessing

If I repeat the timing enough times, every error disappears.

This is a common misconception

Repeating reduces the effect of random errors. It doesn't remove them. Each new reading can still be a bit too big or a bit too small.

Every reading has to go into the mean, even the odd one that is miles off.

This is a common misconception

Anomalous readings should not be used when you calculate an average. Spot the odd one out and leave it out.

My reaction time always makes the time too long.

This is a common misconception

By hand, you might start or stop the timer a little too early or a little too late. Both happen, so you can't tell which way the next error will go.

Timing by hand gives errors that vary from test to test, so I should repeat the timing and use the mean.

This matches the evidence

Yes. Random errors vary in an uncontrolled way and you can't predict whether the next measurement will be too big or too small. Repeat readings reduce their effect.

Random errors are unpredictable. Repeat to reduce their effect, and leave anomalous readings out of the mean.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Time it, repeat it, divide it, and know which speed you've found.

What you need to know

Speed = distance ÷ time. With distance in metres and time in seconds, speed comes out in metres per second (m/s).
Distance ÷ time gives the average speed over the whole distance. Instantaneous speed is the speed at one particular moment, and it can be higher or lower than the average.
To measure speed: mark a measured distance, time it carefully, repeat, take the mean time, then divide the distance by the mean time.

The big picture

Distance ÷ time gives an object's average speed over the whole distance. To measure it well you mark a known distance, time carefully, repeat and take the mean. To catch the speed at one moment (instantaneous speed) you time a very short distance instead.

Key points

1Speed = distance ÷ time gives AVERAGE speed: the total distance divided by the total time taken.

2Instantaneous speed is the speed at one moment. A car's speedometer shows it, and the highest instantaneous speed is the top speed.

3A trolley rolling down a ramp keeps speeding up because a forward force keeps acting on it, so it never moves at one constant speed.

4Count down '3, 2, 1, go' to start the stopwatch at the right moment, and keep your eyes in line with the finish line to stop it at the right moment.

5Repeat the timing and use the mean, but leave any anomalous reading out of the mean.

6Convert distances to metres before working out a speed in m/s. A very short distance timed with an electronic timer gives an estimate of instantaneous speed.

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Worked example

Problem

A sprinter runs a 100 m race in 10 s. What is their average speed?

⚠ Watch out

Thinking an object has just one speed, so that the answer from distance ÷ time (or the speed at the finish line) is 'the' speed. Distance ÷ time gives the average over the whole distance. The speed at any one moment can be higher or lower.

🧠

Memory hook

Average = the whole trip squashed into one number. Instantaneous = a snapshot. To get closer to a snapshot, shrink the distance you time.

✓

Check yourself

In your own words: what is the difference between the number on a car's speedometer and the number you get from distance ÷ time over a whole journey?

Flashcards

(14)

What is the word equation for speed?

speed = distance ÷ time. Distance in metres and time in seconds give speed in metres per second (m/s).

What is average speed?

The total distance an object travels divided by the total time it took: the distance travelled per unit of time.

What is instantaneous speed?

An object's speed at one particular moment in time.

What does a car's speedometer show?

The instantaneous speed, not the average speed.

Is instantaneous speed always the same as average speed?

No. It can be higher or lower than the average speed, because it changes as the object speeds up and slows down.

What is top speed?

The highest instantaneous speed reached during a journey.

Why does a trolley on a ramp not move at a constant speed?

A forward force keeps acting on it, so it keeps speeding up as it rolls.

What does a steeper ramp do to a rolling trolley?

It gives a greater forward force, so the trolley rolls faster.

How can you estimate instantaneous speed?

Time the object over a very short distance (so a very short time) and work out distance ÷ time. For a trolley: markers a few centimetres apart near the end of the ramp, timed with an electronic timer.

Why count down '3, 2, 1, go' when timing?

It helps you start the stopwatch at the right moment.

Where should your eyes be to stop the stopwatch at the finish line?

In line with the finish line. Watching from the side of the line gives a timing error.

How do you find a mean?

Add the values together, then divide by how many values there are.

What is a random error?

An error that varies from test to test in an uncontrolled way: you can't predict whether the next measurement will be too big or too small. Repeat readings reduce its effect.

What should you do with an anomalous reading when you work out an average?

Leave it out of the calculation.

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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From timings to speed

Where does this answer go wrong?

Timing errors

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