Ticker Tape and Motion Graphs, Grade 10
The dots on a ticker tape are a clock, not a ruler.
That one idea is the whole practical. The timer puts a dot down every 0,02 seconds no matter what the trolley does, so every gap on the tape represents exactly the same amount of time. A wider gap therefore means more distance covered in that same slice of time, which means the trolley was going faster.
Nothing else on the tape carries any information. Once you have that, the rest is bookkeeping.
What the tape actually records
South African mains runs at 50 Hz, so a mains-driven ticker timer makes 50 dots every second.
| One dot interval | 0,02 s |
|---|---|
| Ten dot intervals | 0,2 s |
| On the 25 dots per second setting | 0,04 s per interval |
Check this number against your own timer before you calculate anything. Most ticker tape material online is American, built on 60 Hz mains and 1/60 of a second. If you use 1/60 s with South African equipment, every velocity and every acceleration on your sheet is wrong by 20 per cent.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 10 |
| Term | 3 |
| Topic | Topic 7, Mechanics. Motion in one dimension, and motion graphs |
| Status | Prescribed experiment |
| Marks | 56 on our worksheet. None is prescribed |
The two traps in reading a tape
Trap one: the first few dots are rubbish
Every tape starts badly. The timer takes a moment to come up to speed, and the trolley is still being let go. The first two or three intervals are always cramped and uneven.
Ignore them. Run your eye along the tape, find the first clean dot in a stretch that is forming evenly, and call that one A. Nothing before A goes into your table.
Trap two: ten dots is nine intervals
What you measure is the gap, not the dot. Ten dots have nine gaps between them. Count intervals, not dots.
Get this wrong and you have used 0,2 s where the real time was 0,18 s, which is an 11 per cent error running through every number on the page. It is the commonest arithmetic mistake in the whole practical and it is invisible once it is made.
Method
- Thread the tape through the timer and under the carbon disc
- Tape the free end to the back of the trolley
- Switch the timer on first, then release the trolley. In that order, every time. If you release first you lose the start of the run
- Let the trolley run the length of the bench for constant velocity, or down a gentle ramp for the accelerating version
- Switch off and take the tape out
- Find your first clean dot and mark it A. Count ten intervals and mark B. Repeat for C, D, E and F
- Measure the total distance from A to each mark, not the distance between marks
Use a gentle ramp. If it is too steep the trolley is gone before the timer has made enough dots to work with.
The midpoint rule, which almost nobody teaches
The velocity you calculate from A to B is not the velocity at A, and it is not the velocity at B. It is the average across the whole interval.
So it belongs at the middle of that interval in time. If A sits at t = 0 and B at t = 0,2 s, that velocity is plotted at t = 0,1 s.
And for uniform acceleration this is not an approximation. It is exact. When acceleration is constant, the average velocity over an interval is precisely the instantaneous velocity at the midpoint of that interval, which is why the rule works so cleanly.
Plot each velocity at the end of its interval instead and your whole velocity-time graph shifts sideways by 0,1 s. The slope survives, so your acceleration still comes out roughly right, but the intercept is wrong and the error is almost impossible to find afterwards.
A worked tape, with real numbers
A trolley running down a gentle ramp. Distances measured from A, ten intervals apart.
| Point | Time (s) | Distance from A (m) |
|---|---|---|
| A | 0,0 | 0,000 |
| B | 0,2 | 0,080 |
| C | 0,4 | 0,200 |
| D | 0,6 | 0,360 |
| E | 0,8 | 0,560 |
| F | 1,0 | 0,800 |
Now the velocities. Each one is the distance covered in that interval divided by 0,2 s, plotted at the midpoint.
| Interval | Δx (m) | Velocity (m·s-1) | Plotted at t (s) |
|---|---|---|---|
| A to B | 0,080 | 0,40 | 0,1 |
| B to C | 0,120 | 0,60 | 0,3 |
| C to D | 0,160 | 0,80 | 0,5 |
| D to E | 0,200 | 1,00 | 0,7 |
| E to F | 0,240 | 1,20 | 0,9 |
The velocities go up by exactly 0,20 m·s-1 every 0,2 s. That is a useful check on your own tape: if your velocity column climbs by a steady amount, your trolley was accelerating uniformly and your measuring was good.
The acceleration is the slope of the velocity-time graph:
a = Δv ÷ Δt = (1,20 − 0,40) ÷ (0,9 − 0,1) = 0,80 ÷ 0,8 = 1,0 m·s-2
Take the two points from your line of best fit, not from your raw data. The line is the average of all five readings; any two raw points are just two readings.
The three graphs are one story
The slope of one graph is the next graph. Say that once and the whole topic organises itself.
| Graph | Its slope gives you |
|---|---|
| Position against time | Velocity |
| Velocity against time | Acceleration |
For a trolley speeding up steadily, the same motion looks like this three different ways:
| Graph | Shape | Why |
|---|---|---|
| Position-time | A curve, getting steeper | Each second it covers more ground than the last |
| Velocity-time | A straight line, sloping up | The velocity climbs by the same amount every second |
| Acceleration-time | A horizontal line | The rate of climb never changes |
An acceleration-time graph tells you nothing about the motion itself, only about how the motion is changing. Three completely different velocity-time graphs can share one identical acceleration-time graph, as long as all three lines have the same slope. That catches everybody the first time they meet it.
The sign of acceleration, which is where the marks go
"Deceleration" is not a word this syllabus uses
Grade 10 material is blunt about it: decelerate is not a scientific word, and it is best avoided altogether.
Say "speeding up" or "slowing down". Both are changes in velocity, and both are acceleration.
A negative acceleration does not mean slowing down
This is the single biggest trap in the topic. Take a car driving west and braking steadily.
| If you call west positive | If you call east positive | |
|---|---|---|
| The car's velocities are | Positive | Negative |
| The acceleration is | Negative | Positive |
| Is the car slowing down? | Yes | Yes |
Nothing about the car changed. Only the direction you chose as positive changed.
Acceleration tells you how the velocity is changing. On its own it tells you nothing about which way the object is moving, or whether it is speeding up or slowing down.
A learner who has understood that will not lose those marks again. A learner who has memorised "negative means slowing down" will lose them every single year.
The version that needs no ticker timer at all
This is the experiment the curriculum actually prescribes, and it uses a courtyard, a stopwatch and ten bags of soil.
- Draw a chalk line 7 to 10 m long outside, or scratch one in the sand
- Put a tablespoon of soil into each of ten small bags and close them so they do not burst
- One learner walks beside the line at a slow, steady pace. Small slow steps are much easier to keep steady than long ones
- A second learner calls "now" every two seconds. On each call the walker drops one bag beside the line, hand down at their side
- Afterwards, measure the position of each bag from the start and tabulate time against position
- Plot position against time and describe the shape in words
The learner is the trolley. The voice is the timer. The bags are the dots.
Once a class has walked it, a ticker tape stops being a mysterious strip of paper. A learner who has been the trolley knows exactly what the dots are, and the timer becomes an obvious labour-saving device rather than a new idea to learn. Run this one first even if you own a ticker timer.
And the data will not be perfect, which is the point. A typical set of intervals from a walk described as "constant pace" comes out as 0,80, 0,92, 0,83, 0,83, 0,67 and 0,95 m. That is nearly a 30 per cent spread. Asking the class where that spread came from is a better question than anything a clean tape can offer.
What you need
| Item | Qty | Why |
|---|---|---|
| Ticker tape timer, dual speed 25/50 dots per second | 1 | The instrument. Use the 50 setting on South African mains |
| Ticker tape roll | 2 | The consumable. A class of thirty gets through a roll faster than anyone expects |
| Ticker tape carbon disc, pack of 100 | 1 | The other consumable. No disc, no dots |
| Dynamics trolley, pair | 1 pr | The moving object |
| Dynamic track | 1 | A straight, smooth run. A bench works, a track works better |
| Digital stopwatch | 4 | For the walking method, and for every other mechanics practical in the school |
| Tape measure, 5 m steel | 2 | Measuring positions along the chalk line |
| Retort stand base and rod | 1 | Raising one end of the track to a gentle, repeatable angle |
The tape and the carbon discs are the two things that run out, and the two things nobody checks until the period has already started. Order them deeper than you think you need.
Sandwich bags, soil and chalk are not on the list on purpose. Every school has all three, and posting soil would be absurd.
What you should see
- Evenly spaced dots for a trolley moving at constant velocity along a flat bench
- Dots that spread out steadily for a trolley running down a ramp
- A cramped, uneven start on every single tape. That is normal and it gets ignored
- A velocity column that climbs by roughly the same amount each interval
- A position-time curve, a velocity-time straight line, and an acceleration-time flat line
If it does not work
| What happens | What caused it |
|---|---|
| No dots at all | The carbon disc is worn out, or in upside down. This is the first thing to check, always |
| Dots in one spot, a hole in the tape | The trolley was released before the timer was switched on, or the tape jammed |
| The first few intervals are a mess | Normal. The timer is coming up to speed and the trolley is still being let go. Start from a clean dot |
| The tape drags and the trolley slows | The tape is catching on the timer or the bench. Feed it straight, and keep the roll ahead of the trolley |
| The trolley is gone before there are enough dots | The ramp is too steep. Lower it until the run takes about a second |
| Velocities do not climb steadily | Measuring from the wrong reference. Every distance is measured from A, not from the previous mark |
| The acceleration comes out far too large or small | Check the frequency. 0,02 s per interval on 50 Hz, not 1/60 s |
| The velocity-time graph does not start at zero | Correct, if the trolley was already moving when the first clean dot was made |
| The walking graph is a staircase | The walker is marching to the count. Small, slow, steady steps |
Safety
This is the lowest-hazard practical in the Grade 10 range. No chemicals, nothing hot, no goggles.
- The ticker timer runs off the mains. Check the lead and the plug before the lesson, and keep it away from water
- Put a book or a hand at the end of the bench so the trolley does not launch itself onto the floor
- Nobody stands in front of a loaded ramp
- For the walking method, watch where you are going. A learner walking a chalk line while dropping bags is not looking out for the step or the drain
- Wash hands after handling soil
How the 56 marks are made up
| Section | Marks |
|---|---|
| Reading the tape: intervals, frequency and the first dots | 8 |
| The displacement table | 8 |
| Velocity, including the midpoint rule | 10 |
| The three graphs, and acceleration from the slope | 9 |
| The sign of acceleration | 9 |
| The walking method, with real data to process | 8 |
| Conclusion | 4 |
No mark allocation is prescribed for this practical. The worksheet and this split are ours.
The two marks most often dropped are the midpoint column and the axis labels. Both are avoidable and both cost a mark every time.
Close behind: giving an acceleration with no direction. Acceleration is a vector, and a bare number is half an answer.
If you have time
Cut the tape into its ten-interval strips and paste them side by side on a sheet, in order. The tops of the strips form the velocity-time graph directly, because each strip's length is proportional to the velocity in that interval. The graph builds itself out of the tape, and it is the fastest way to make the connection visible.
Run one tape with the trolley moving at constant velocity and paste it next to the accelerating one. Even spacing against widening spacing, on one sheet, is worth more than any diagram.
Ask what the tape would look like for a trolley slowing down. The dots bunch up. Then ask whether that is a negative acceleration, and watch the argument start.
Free worksheet and marking memo
Both free, no sign up, straight to the PDF.
- Learner worksheet, 56 marks, with the interval calculations, the velocity table and its midpoint column, all three graphs, the sign-of-acceleration questions and a real set of walking data to process
- Marking memorandum, with worked answers, how to mark a graph drawn from a learner's own tape, and the four answers that look right and score nothing
Related practicals
- Acceleration on an inclined plane, Grade 10. The same measurement with a stopwatch and a ramp instead of a timer, plus what happens when you change the angle or the surface
- Conservation of energy with a pendulum, Grade 10. Same term, same stopwatch, energy instead of motion
- Newton's Second Law, Grade 11. Where the trolley and track go next year, with a force added
- Conservation of linear momentum, Grade 12. And the year after that, on the same track
- Vertical projectile motion, Grade 12. Where the equations of motion take over from the graphs
Buy this experiment
We are putting together a Motion and Graphs Kit for Grade 10 with the ticker timer, tape, carbon discs, trolley, track, stopwatches and tape measures in one box, plus a printed teacher guide and the marking memo. Coming shortly.
The two lines to buy first are the cheapest ones: the tape roll and the carbon discs. If your school already owns a ticker timer, those two are the only things standing between you and running this practical, and they are the two that are always missing when the period starts.
The trolley and the track are worth buying once and using for three years. The same pair runs this practical in Grade 10, Newton's Second Law in Grade 11 and conservation of momentum in Grade 12. Very little else in a school physics cupboard earns its keep across three grades.
And if you have no ticker timer at all, you can still run the prescribed experiment this week. It needs a stopwatch, a tape measure and a courtyard.