Velocity-time graphs with a ticker-timer
Students create velocity-time graphs from their own measurements for different kinds of motion. In a qualitative way only, the significance of gradient is emphasized.
Apparatus and materials
Runway, with means to produce a uniform slope
Tricker-timer with power supply unit
Health & Safety and Technical notes
Trolley runways are heavy. Do not expect one technician to be able to manipulate and carry one unaided. If the load presented by one end is less than 10 kg, one runway could be carried by two 15-year olds.
Accelerating down a slope
a Set up the runway with a significant slope, with a buffer at the bottom to catch the trolley.
b Test what happens when you put a trolley on it. It should accelerate down the slope.
c Thread a length of ticker-tape, about the same length as the trolley's journey down the slope, through the ticker-timer. Stick the end of the tape to the trolley.
d Turn the ticker-timer on, and allow the trolley to accelerate down the slope.
e Cut the tape through the dot (or set of overprinted dots) produced just before the trolley was released. Count ten dot-to-dot spaces and cut the tape again. (If the dots are too close together to distinguish them, then you will have to estimate the ten spaces.) Starting from your last cut, count ten more spaces, and cut again.
Repeat this, until you have a collection of consecutive tapes, each one longer than the one before it. Number the order of your tapes, from 1 onwards.
f Draw a horizontal line on a sheet of paper. Make a 'bar chart' by sticking the tapes vertically side by side, so that their bottoms just touch the horizontal line. The first and shortest tape should be at the left hand end of the line.
g The horizontal line acts as a time axis, with its left end time zero. Mark your horizontal axis in intervals of 0.2 seconds, and add a suitable axis label.
h Draw a vertical line through the zero of the time axis. This vertical line is the velocity axis. When time was zero for the trolley journey, velocity was zero. (The trolley started from standstill, or rest.)
i Mark the scale on the vertical axis, in centimetres per second. Each vertical centimetre represents 5 centimetres per second of speed.
j Draw a smooth line through the top-centre of each tape on your velocity-time graph. Describe in words what the graph says about the trolley motion.
Constant velocity on a slope
k Reduce the slope of the runway. Adjust it so that, when you give the trolley a brief gentle push, it travels for a large part of the runway length without slowing down or speeding up. The forces of gravity and friction are now balanced.
l Produce a set of ten-tick-tapes for a steady velocity (or approximately steady velocity) journey of the trolley.
m Make a velocity-time chart as before, using at least five consecutive ten-tick-tapes for a section of the journey for which velocity is constant. (Ignore the first tape, or tapes, when the trolley was accelerating as you pushed it. Ignore tapes for later motion if there is a lot of change in velocity.)
Motion up a slope
n Move the ticker-timer, and the trolley, to the lower end of the runway. Give the trolley a short push, so that it moves up the slope. Predict what the velocity-time graph for this motion will look like.
o Test your prediction by making a velocity-time graph with a suitable set of ten-tick-tapes.
(As for the previous case, ignore lengths of tape that were made while you were pushing. Choose time zero as some time soon after your push.)
p Draw a smooth line through the top-centre of each tape on your velocity-time graph. Describe in words what the graph says about the trolley motion.
1 There is a lot of activity here, and you may need more than one lesson.
2 If your ticker-timers use a carbon disc, tell students to be sure to pass the tape under the disc. If you are using photosensitive tape, explain that they must wait a few minutes after a run for the dots to appear.
3 The whole procedure above assumes that the ticker-timers produce 50 dots per second (mains frequency of the AC voltage driving them). If your ticker-timer produces more dots per second (some produce 100 dots per second) you will have to change the text.
You will need to explain that the ticker-timer makes dots at regular intervals. You could say:
Each period between dots is a 'tick' of time. A low voltage alternating at the same frequency as mains (50 Hz) drives the ticker-timer. If the ticker-timer produces 50 dots per second, then a tick is equal to 1/50 or 0.02 seconds.
4 Step i of the procedure: The length of each tape is the number of centimetres that the trolley travelled in a fifth of a second, or 0.2 seconds. So students could multiply the length by 5 to find the velocity of the trolley in centimetres per second. The actual lengths of the tapes are fixed proportions of the velocity.
5 Once students have completed their first velocity-time graph, discuss what it means. The bigger the acceleration, the steeper the slope of the graph. The gradient of the line is always equal to the value of the acceleration. If the line is straight, then the acceleration is constant (or 'uniform'). If it curves then acceleration varies.
6 More advanced students could find the gradient of the graph quantitatively. If the graph is curved, they should draw tangents and find the gradient at more than one point.
When finding gradients, big triangles produce more accurate results (and they are easier to measure).
7 You might ask students how to use the tapes to construct distance-time (or displacement-time) graphs. The cumulative lengths of the tapes show total distance travelled.
An important point is that the same motion can be represented in two related but significantly different ways, by distance-time (or displacement-time) as well as velocity-time graphs.
8 The second velocity-time chart shows a trolley moving at constant velocity. The top of the tape chart is horizontal and the gradient is zero, indicating there is no acceleration.
9 The third velocity-time chart shows a trolley decelerating up the slope. The gradient of the chart is negative.
This experiment was safety-checked in December 2004