# Ticker Tape Timer Analysis - acceleration by successive differences, v–t graph

> Simulate a ticker-tape timer: generate tapes, measure counting points, get speeds and acceleration by successive differences, plot v–t and cut-tape charts.

- URL: https://qilingtools.com/en/physics/ticker-tape
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

A simulated electromagnetic ticker timer and spark timer pulling a paper tape. Pick uniform, accelerating, decelerating or custom v₀ and a, change the mains frequency and how counting points are chosen, and add random measuring error. A draggable ruler and a zoomed view let you read each counting point; the tool then lists segment lengths, mid-time speeds and the acceleration by successive differences, with every substitution written out. The analysis page plots a fitted v–t graph and a cut-tape chart and shows what typical mistakes, such as using T = 0.02 s or forgetting cm to m, would give.

## How to use

1. Choose the motion (or drag v₀ and a), the counting-point spacing and the frequency
2. Press Run to watch the cart pull the tape through the timer
3. Drag the ruler, tap a counting point to zoom, and check the table of readings and speeds
4. Open Data analysis for the graphs and working, or Practice for random tape problems

## Features

- Animated electromagnetic and spark timers with slow motion
- Counting periods of 0.02 s, 0.04 s or 0.1 s, plus optional random reading error
- Draggable ruler and zoom on each counting point, read to 0.1 mm
- Mid-time speeds and successive-difference acceleration with full working (odd segment dropped)
- Fitted v–t graph, cut-tape chart and Δx table to test for uniform acceleration
- Typical-mistake comparison and random tape problems with instant marking

## FAQ

### What is the counting period T?

At 50 Hz the timer prints a dot every 0.02 s. If there are five intervals between neighbouring counting points (four dots not shown), T = 5 × 0.02 s = 0.1 s. Using 0.02 s by mistake makes the acceleration 25 times too large, the most common error in this experiment.

### Why group the segments in the successive-difference method?

For uniform acceleration the difference between successive equal-time displacements is constant, Δx = aT². Averaging neighbouring differences cancels the middle data and leaves only the first and last segments. Grouping six segments as a = [(x₄ + x₅ + x₆) − (x₁ + x₂ + x₃)] / 9T² uses every measurement. With four segments a = [(x₃ + x₄) − (x₁ + x₂)] / 4T²; with an odd number, drop one first.

### How do I find the speed at a counting point?

In uniformly accelerated motion the speed at the middle instant of an interval equals the average speed over it. So vₖ = (xₖ + xₖ₊₁) / 2T, using the two segments either side of point k, converted to metres: (4.03 + 6.00) cm / 0.2 s = 0.502 m/s.

### What is the difference between the electromagnetic timer and the spark timer?

The electromagnetic timer runs on about 8 V AC and a vibrating pin marks the tape through carbon paper. The spark timer runs on 220 V AC and marks with a spark and toner disc, with less friction. Both print every 0.02 s at 50 Hz and neither works on DC. Switch the timer on before releasing the cart.

### How does the cut-tape chart relate to the v–t graph?

Each strip spans the same time T and its length is the average speed in that interval times T. Standing the strips side by side, the midpoints of their tops trace the v–t graph scaled by 1/T. A straight sloping line means uniform acceleration, and the slope of a fitted v–t line is the acceleration.

## Related tools

- [Unit Converter](https://qilingtools.com/en/math/unit): Free online unit converter: length, area, volume, weight, temperature, time, speed, data, pressure, energy and angle — one value converts every unit at once.
- [Vector Calculator](https://qilingtools.com/en/math/vector): Free online vector calculator for 2D and 3D: addition, scalar multiples, dot and cross products, magnitude, angle, unit vector and projections, with checks.
- [Significant Figures Calculator](https://qilingtools.com/en/math/significant-figures): Free online sig fig calculator: count significant figures digit by digit, round to N sig figs or decimals with six rounding modes, and compute by sig fig rules.
- [Tone Generator](https://qilingtools.com/en/audio/tone-generator): Free online tone generator: sine, square, sawtooth and triangle waves from 1 to 20,000 Hz, a note picker, sweeps, white/pink/brown noise and a WAV download.
- [Audio Spectrogram](https://qilingtools.com/en/audio/spectrogram): Free online spectrogram generator: see time, frequency and level from a Hann-windowed STFT, with FFT size, log axis, dB range and colour maps. Exports PNG.
- [Decibel Meter](https://qilingtools.com/en/audio/decibel): Free online decibel meter: measure noise with your mic in real time, A/C/Z weighting, fast/slow response, min/max/average/Leq, 60-second graph and calibration.
- [Physics Formula Calculator](https://qilingtools.com/en/physics/physics): Physics formulas solved with steps: SUVAT, projectiles, Newton’s laws, inclines, energy, Ohm’s law, resistors, RC, buoyancy, waves, lenses, gravity.
- [Fourier Series & FFT Visualizer](https://qilingtools.com/en/math/fourier): Fourier series coefficients and animated partial sums for square, sawtooth, triangle or any function (Gibbs), draw-your-own epicycles and FFT spectra.