Δ Fig. 1.5 You can use a stopwatch to measure the time taken to run a certain distance.
To study almost anything about the world around us or out into Space, we will need to describe where things are, where they were and where we expect them to go. It is even better if we are able to measure these things. Only when we have an organised system for doing this will we be able to look for the patterns in the way things move – the laws of motion – before going a step further and suggesting why things move as they do – using ideas about forces.
Think about being a passenger in a car travelling at 90 kilometres per hour. This, of course, means that the car (if it kept travelling at this speed for 1 hour) would travel 90 km. During 1 second, the car travels 25 metres, so its speed can also be described as 25 metres per second. Scientists prefer to measure time in seconds and distance in metres. So they prefer to measure speed in metres per second, usually written as m/s. KNOWLEDGE CHECK ✓ Know how to measure distances and times accurately. ✓ Know how to calculate the areas of a rectangle and a triangle. ✓ Know how to plot a graph given particular points. ✓ Know how to substitute values into a given formula. LEARNING OBJECTIVES ✓ Deﬁne speed and calculate average speed from total distance divided by total time. ✓ Be able to plot and interpret a speed–time graph and a distance–time graph. ✓ Recognise from the shape of a speed–time graph when a body is at rest, moving with constant speed or moving with changing speed. ✓ Be able to calculate the area under a speed–time graph to work out the distance travelled for motion with constant acceleration. ✓ Demonstrate an understanding that acceleration and deceleration are related to changing speed, including qualitative analysis of the gradient of a speed–time graph. ✓ State that the acceleration of free fall g for a body near to the Earth is constant.
✓ EXTENDED Distinguish between speed and velocity. ✓ EXTENDED Deﬁne and calculate acceleration using change of velocity divided by time taken. ✓ EXTENDED Calculate acceleration from the gradient of a speed–time graph.
✓ EXTENDED Recognise linear motion for which the acceleration is constant and calculate the acceleration. ✓ EXTENDED Recognise motion for which the acceleration is not constant.
CALCULATING SPEED The speed of an object can be calculated using the following formula: distance speed = time s v= t where: v = speed in m/s, s = distance in m, and t = time in s. Most objects speed up and slow down as they travel. An object’s ‘average speed’ can be calculated by dividing the total distance travelled by the total time taken. REMEMBER
Make sure that you can explain why this is an average speed. You need to talk about the speed not being constant throughout, perhaps giving specific examples of where it changed. For example, you might consider a journey from home to school. You know how long the journey takes and the distance between home and school. From these, you can work out the average speed using the formula. However, you know that, in any journey, you do not travel at the same speed at all times. You may have to stop to cross the road, or at a road junction. You may be able to travel faster on straight sections of the journey or round corners.
WORKED EXAMPLES 1. Calculate the average speed of a motor car that travels 500 metres in
20 seconds. Write down the formula:
Substitute the values for s and t:
v = 500 / 20
Work out the answer and write down the units:
v = 25 m/s
◁ Fig. 1.6 Cover speed to ﬁnd that speed = distance/time.
2. A horse canters at an average speed of 5 m/s for 2 minutes.
Calculate the distance it travels. Write down the formula in terms of s:
Substitute the values for v and t:
s = 5 × 2 × 60
Work out the answer and write down the units:
s = 600 m
◁ Fig. 1.7 Cover distance to ﬁnd that distance = speed × time.
ARE SPEED AND VELOCITY THE SAME? We often want to know the direction in which an object is travelling. For example, when a space rocket is launched, it is likely to reach a speed of 1000 km/h after about 30 seconds. However, it is extremely important to know whether this speed is upward or downward. You want to know the speed and the direction of the rocket. The velocity of an A object is one piece of information, but it consists of two +10 m/s parts: the speed and the direction. In this case, the velocity of the rocket is 278 m/s (its speed) upward (its direction). B A velocity can have a minus sign. This tells you that the – 10 m/s object is travelling in the opposite direction. So a velocity of –278 m/s upward is actually a velocity of 278 m/s downward. Δ Fig. 1.8 Both cars have the same speed. Car A has a velocity of +10 m/s The diagram shows two cars with the same speed but and car B has a velocity of –10 m/s. opposite velocities. END OF EXTENDED
QUESTIONS 1. Imagine two cars travelling along a narrow road where it is not possible to pass each other. Describe what would happen when:
a) both cars have a velocity of +15 m/s b) one car has a velocity of +15 m/s and the other –15 m/s
c) both cars have a velocity of –15 m/s. 2. You walk to school and then walk home again. What is your average velocity for the whole journey? Be careful.
3. A journey to school is 10 km. It takes 15 minutes in a car. What is the average speed of the car?
4. How far does a bicycle travelling at 1.5 m/s travel in 15 s? 5. A person walks at 0.5 m/s and travels a distance of 1500 m. How long does this take?
USING GRAPHS TO STUDY MOTION Journeys can be summarised using graphs. The simplest type is a distance–time graph, where the distance travelled is plotted against the time of the journey. At the beginning of any measurement of motion, time is usually given as 0 s and the position of the object as 0 m. If the object is not moving, time increases but distance does not. This gives a horizontal line. If the object is travelling at a steady speed, then both time and distance increase steadily, which gives a straight line. If the speed is varying, then the line will not be straight. You can calculate the speed of the object by finding the gradient of the line on a distance–time graph. In Fig. 1.9, which shows a bicycle journey, the graph slopes when the bicycle is moving. The slope gets steeper when the bicycle goes faster. The slope is straight (has a constant gradient) when the bicycle’s speed is constant. The cyclist falls off at about 142 metres from the start. After this, the graph is horizontal because the bicycle is not moving. 160 140
120 100 80 60 40 20 0
graph curves as bicycle speed increases
time/s straight line as bicycle speed is constant
60 bicycle stops suddenly
80 bicycle not moving
Δ Fig. 1.9 A distance–time graph for a bicycle journey.
QUESTIONS 1. How can you tell from a distance–time graph whether the object was moving away from you or toward you?
2. Very often we use sketch graphs to illustrate motion. Describe
3. Sketch a distance–time graph for a bicycle travelling downhill.
the main differences between a sketch graph and a graph.