Students should learn:
- how to interpret the gradient of a distance–time graph
- how to calculate the speed of an object using the speed formula
- how to use a distance–time graph to compare the speeds of different objects.
- state that the gradient of a distance-time graph represents the speed
- use the speed formula to calculate the average speed of an object.
- rearrange and use the speed formula compare the speed of different objects using the gradient of a distance–time graph.
Teacher notes: Motion
Extension: Distance–time gradient calculations
Support: What is my distance–time graph?
Bump up your grade: What is my distance–time graph?
Lesson structure / Support, Extend and Practical notes
Starters
Understanding graphs – Show the students slides of a range of graphs showing the relationship between two variables and ask them to describe what is happening. Use this activity to support students and ensure that they understand the key terms used in describing a graph (the axes and gradient). You can extend students by giving more complex examples leading to ideas such as an increase in rate (changes of gradient).(5minutes)
Speedy start – Give the students a set of cards showing different moving objects and ask them to put them in order from fastest to slowest. Add some data on the objects so that the students can actually work out the speed of the objects using the speed formula. Examples could be a worm (0.5 cm/s), human walking (0.5 m/s), bicycle (5 m/s), car(20 m/s), passenger jet (200 m/s), and missile (1 km/s). (10 minutes)
Main
Some students have difficulty understanding what you mean by the term ‘object’ and you will have to exemplify this idea by talking about cars, trains or runners. Students can also have difficulty with the whole idea of a ‘time axis’. You might like to show time as moving on by revealing the graph from left to right, and discussing what is happening to the distance the object has moved over each second.
There are quite a few who fail to understand that the horizontal portions of the graph show that the object is stationary. Emphasise that the distance isn’t changing, even though time is; ‘the object hasn’t got any further away during this second so it must be still’. You should use additional simple graphs to discuss the motion of several objects until you are sure that the students can identify when the objects are moving fastest.
The students should be familiar with the speed equation, but it may have been some time since they used it in KS3. A few practice questions should remind them of the basic idea. Be very cautious of students using inappropriate units for speed such as ‘mph’ or even ‘m/s’ (metres per second). If students find ‘per’ difficult, then just use ‘each’.
To extend students, you can get them to read information off the graphs to calculate speed, although this is covered in detail in a later lesson at an appropriate level. They should be able to calculate the overall average speed and the speed during individual phases of the motion.
You should also extend students by discussing displacement instead of distance, or you could leave this until you are discussing velocity in the next topic.
The practical activity is a good way to round off the lesson, and it can be as brief as 10 minutes long if bicycles are not involved.
Plenaries
Record breakers – The students should analyse data about the 100 m sprint records (or other records such as swimming). They can try to find out if there appears to be a continuous improvement in running speeds or if there are leaps where the records change suddenly. They can also discuss the precision of the records and link this to improvements in timing technology.(5 minutes)
A driving story – Give the students a paragraph describing the motion of a car through a town, including moving at different speeds and stopping at traffic lights, etc. Ask them to sketch a graph of the described motion. Students can be supported by giving them the graph and asking for them to generate the story or extended by providing numerical information that has to be plotted accurately. (10 minutes) / Support
Construct graphs one section at a time so that the students can fully understand one part of the graph before moving on to the next part of the motion. Build up the complexity of the graphs as the lessons in this section of the course continue.
Extend
Using the details from the train timetable (see ‘Further teaching suggestions’ for ‘Calculating speeds’) the students can plot graphs to compare the speeds of local trains and express trains.
Practical support
Be a distance recorder!
Measuring speed is a simple activity and livens up what can be a fairly dry start to the ‘Motion’ chapter.
Equipment and materials required
For each group: stopwatch, metre wheel. Clipboards and marker cones are also useful.
Details
The students should measure out distances first and then time each other walking, running, hopping or riding over these fixed distances. An outdoor netball court, or similar, can provide a set of straight and curved lines for the students to follow. You may like to see if the students travel faster along the straight edges or if they follow the curves on the court. If you intend to use bicycles, then a lot more space will be needed and the students must wear the appropriate safety gear. Check with the PE department to see if they have cones to mark out the distances and if they mind bicycles on their running tracks or shoes on their indoor courts!
Course / Subject / Topic / Pages
Additional science / Physics / P2 1.1Distance–time graphs / Pages 166–167
Learning objectives / Learning outcomes / Specification link-up / Kerboodle
Students should learn:
- that velocity is the speed in a particular direction
- that acceleration is the rate of change of velocity.
- explain the difference between the velocity of an object and the speed
- calculate the acceleration of an object using the acceleration equation.
- rearrange and use the acceleration equation.
The acceleration of an object is given by the equation: [P2.1.2 e)]
Controlled Assessment: AS4.3 Collect primary and secondary data. [AS4.3.2 d)] / How science works: Acceleration of a trolley (P2 1.2)
Lesson structure / Support, Extend and Practical notes
Starters
Getting nowhere fast – A racing driver completes a full circuit of a 3 km racetrack in 90 seconds. Ask: ‘What is his average speed? Why isn’t he 3 km away from where he started?’ Demonstrate this idea to explain the difference between distance travelled and displacement. Lead on to a discussion about objects that are moving but do not get further away from the origin as they are following closed paths. (5 minutes)
Treasure island – Give the students a scaled map with a starting point, hidden treasure, protractor and a ruler. At first, only give them the times they have to walk for, then the speeds they must go at, and finally the matching directions. See which group can find the treasure first. This shows how important direction is when describing movement. Support students by starting with very simple examples. Extend students by asking them to produce a set of instructions to get to a treasure chest while avoiding a set of obstacles such as the ‘pit of peril’. (10 minutes)
Main
Talking about fairground rides or roundabouts helps to get across the idea that you can be moving at a constant speed but be feeling a force. You can link this experience into the idea that unbalanced forces cause acceleration, see later topics.
Some students will not be clear about the difference between speed and velocity, and a few examples are needed. These can include simply walking around the room and describing your velocity as you go in one direction or another.
You might like to discuss a collision between two cars travelling at 45 and 50 km/h. If they collide while travelling in opposite directions the impact will be devastating, because the relative velocity is 95 km/h. If they collide when they are travelling in the same direction only a ‘nudge’ will be felt, because their relative velocity is only 5 km/h. Clearly, the direction is very important. Check that all of the students can give an example of a velocity.
Velocity–time graphs look similar enough to distance–time graphs to cause a great deal of confusion for students. Because they have just learned that the horizontal region on a distance–time graph shows that the object is stationary, they will probably feel that this is true for the velocity–time graph too. Time should be taken to explain that the object is moving at a steady velocity.
As usual, some students will take the calculations in their stride while you may need to provide extra support for others. When using v and u as symbols in equations, be very careful that the students are discriminating between them clearly.
Many students are unclear on the units for acceleration (m/s2) and ask what the ‘squared bit’ is. If they are mathematically strong, you might like to show where the unit comes from, using the equation, but otherwise they should not worry about it. Always check that they are applying the unit correctly.
There may be some confusion with the terms ‘acceleration’, ‘deceleration’ and ‘negative acceleration’, especially if you consider objects that move backwards as well as forwards. To extend students, you can show a graph of the motion of an object moving forwards then backwards, and describe the acceleration in detail.
Plenaries
Comparing graphs – Ask the students to make a comparison of what a distance–time graph and a velocity–time graph show. They should produce a chart/diagram that could be used to show another group of students the similarities and differences, highlighting the distinctions between what the gradients of these graphs represent. (5 minutes)
Accelerated learning – The students should try a few additional acceleration questions. They might be supported using simple structured questions, or extended by asking for calculations involving the rearrangement of the basic acceleration equation.(10 minutes) / Support
The difference between speed–time and distance–time graphs should be reinforced. You might want to use different colour sets to plot the graphs to make them visually different.
Extend
Extend students by asking them to look into the details of the concepts of displacement and velocity. Ask: ‘What is the average speed of a Formula One car over one whole lap? What is the average velocity for the complete lap?’ The students could draw a diagram to explain the difference.
Course / Subject / Topic / Pages
Additional science / Physics / P2 1.2 Velocity and acceleration / Pages 168–169
Learning objectives / Learning outcomes / Specification link-up / Kerboodle
Students should learn:
- how to interpret the gradient of a velocity–time graph
- how to calculate the distance travelled by an object from the area under a velocity–time graph. [HT only]
- explain how data-logging equipment can be used to measure the velocityof an object
- describe the acceleration of an object from a velocity–time graph.
- use velocity–time graphs to compare accelerations
- use velocity–time graphs to compare distance travelled. [HT only]
Calculation of the acceleration of an object from the gradient of a velocity–time graph. [P2.1.2 g)] [HT only]
Calculation of the distance travelled by an object from a velocity–time graph.
[P2.1.2 h)] [HT only]
Controlled Assessment: AS4.3 Collect primary and secondary data. [AS4.3.2 a)]; AS4.5 Analyse and interpret primary and secondary data. [AS4.5.3 a)] / Bump up your grade: Velocity–time graph: Using motion graphs to show how fast things move
Extension: Velocity–time gradient calculations
Lesson structure / Support, Extend and Practical notes
Starters
Late again? – Give the students the distance from their last class to the laboratory and ask them to work out their speed on the journey to you, using the time it took them to arrive. You can provide some example distances from other likely rooms if they have no idea about how far it is between places (surprisingly common). Anybody travelling at less than 1 m/s clearly isn’t keen enough! (5 minutes)
Finding areas – Get the students to calculate the total area of a shape made up of rectangles and triangles. Students can be extended by asking them to find the total areas of more complex graphs, while others can be supported by providing graphs in which the shape has already been broken down into basic rectangles and triangles. (10 minutes)
Main
Demonstrate the results produced for test A in the Student Book. If you do not get a straight line, you might want to discuss air resistance as a force opposing the movement of the trolley.
The investigation into the motion of an object is a good one if you have sufficient equipment. Alternatives using light gates do not give a simple comparison of the accelerations, but you may be able to demonstrate that the velocity has increased. (This relates to: How Science Works: types of variable; fair testing; relationships between variables.)
As before, time should be taken to ensure that the students understand what the gradients of the different graphs mean. They should be encouraged to break the graph down and just look at one section at a time, in order to explain what is happening between these sections. Real motion may not produce straight lines and simple gradients, but these are the best to use in examples for now.
There should be no difficulty explaining that braking will reduce the velocity of the car, but you might like to ask what braking would look like on the graph if the car was in reverse. The change can confuse some students.
Using the area under the graph to find the distance travelled is commonly forgotten, so try a couple of examples and refer back to it in later lessons. When calculating the area, ensure that the students are not giving their answers as ‘distance =15 cm², or similar. This can happen when they ‘count boxes’ or do their calculations based on the area being measured in centimetres. Make sure that they are reading the distances and times off the graph, not the actual dimensions of the shapes. [HT only]
Finally, you could show what would happen if the deceleration took longer, by superimposing the new gradient over the old one and showing that the area is greater.
Plenaries
Busy teacher – Wear a pedometer throughout the lesson, calculate your average step distance and then ask the students to work out how far you have moved and your average speed. A typical example stride distance is 0.5 m with somewhere between 400 and 600 paces per lesson, giving a distance of 200 to 300 m in 1 h. The students could estimate their average daily speed too. (5 minutes)
Comparing graphs – Ask the students to describe the differences in the movement of three cars as shown on the same velocity–time graph. You can also use distance–time graphs. These comparisons should cover the speeds at different times and even the acceleration of the cars over periods by comparing the gradients. Support students by taking them through the examples step by step. Students can be extended by asking them to read data from the graphs (such as starting speed and final speed) and attempt to calculate the acceleration. (10 minutes) / Support
Focus on the basics of measuring the area, reminding the students of the calculations needed to find the area of the triangular parts. Watch out for students reading incorrect values from the graphs; instead of reading the changes they can often just read the higher value.
Extend
The students should look at the effect of aerodynamics on motion; it is air resistance that makes the motion of objects much more complex. They should find out about how these effects are investigated.
Practical support
Investigating acceleration
Dynamics trolleys are an excellent way of studying motion, but class sets are very expensive. If none are available, then fairly large toy cars can be used for the basic experiments. Velocity sensors are also expensive and you may need to modify this experiment into a demonstration.
Equipment and materials required
Dynamics trolley, adjustable slope, protractor and data-logging equipment including a velocity sensor.
Details
Set up the equipment so that the angle of the ramp can be adjusted and easily measured. Make sure that the sensor is pointing along the path of the slope as otherwise the velocity will not be measured accurately. The students activate the sensor and then release the trolley. Repeating this for a range of slope angles should give the result that the steeper the slope the greater the acceleration.