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.

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

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.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Ticker Tape Timer Analysis

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

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.

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

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