Describing motion along a line

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	Time: 15 hours Level: Intermediate

	Introduction Introduction Resource Motion is vital to life, and to science. In many ways it was the investigation of motion, initiated by Galileo Galilei in the late sixteenth century, and brought to a head by Isaac Newton in the seventeenth,...

	The description of motion The description of motion Resource The concepts that have been developed to allow the description of motion – concepts such as speed, velocity and acceleration – are now so much a part of everyday language that we rarely think about them....

	1 From drop-towers to Oblivion – some applications of linear motion 1 From drop-towers to Oblivion – some applications of linear motion Resource We have all experienced that momentary feeling of lightness when an elevator begins its downward motion. It is almost as if our weight had suddenly been reduced or, conceivably, that the pull of the Earth's...

	2 Positions along a line 2.1 Simplification and modelling Resource Everyday experience teaches us that unconfined objects are free to move in three independent directions. I can move my hand up or down, left or right, backwards or forwards. By combining movements in these... 2.2 Describing positions along a line Resource To take a definite case, consider a car moving along a straight horizontal road. The car can be modelled as a particle by supposing the particle to be located at, say, the midpoint of the car. It is clearly... 2.3 Position–time graphs Resource Tables do not give a very striking impression of how one thing varies with respect to another. A visual form of presentation, such as a graph, is usually much more effective. This is evident from Figure... 2.4 Displacement–time graphs Resource A particle's position, x, is always measured from the origin of the coordinate system. However, in describing real motions it is often important to know where something is located relative to a point other... 2.5 A note on graph drawing Resource There will be many occasions throughout your study of physics when you will need to draw graphs. This subsection gives some important guidelines for this activity.

	3 Uniform motion along a line 3.1 Describing uniform motion Resource Uniform motion along a line is the very special kind of motion that occurs when an object moves with unvarying speed in a fixed direction. During a fixed period of time, such as one second, an object... 3.2 Constant velocity and the gradient of the position–time graph Resource Two things you will almost certainly want to know about any particle undergoing uniform motion are ‘how fast is it travelling?’ and ‘in which direction is it moving?’ The physical quantity that provides... 3.3 Initial position and the intercept of the position–time graph Resource The uniform motion of a particle is such a simple form of motion that apart from enquiring about the particle's velocity, the only other kinematic question you can ask is ‘where was the particle at some... 3.4 The equations of uniform motion Resource It has already been said that the straight-line graph of any uniform motion can be represented by an equation of the general form 3.5 Velocity–time and speed–time graphs Resource Just as we may plot the position–time graph or the displacement–time graph of a particular motion, so we may plot a velocity–time graph for that motion. By convention, velocity is plotted on the vertical... 3.6 The signed area under a constant velocity–time graph Resource There is a simple feature of uniform velocity–time graphs that will be particularly useful to know about when we come to consider non-uniform motion in the next section. It concerns the relationship between... 3.7 A note on straight-line graphs and their gradients Resource We end this section by reviewing some of the important features of straight-line graphs, though we do so in terms of two general variables z and y, rather than x and t, in order to emphasise their generality....

	4 Non-uniform motion along a line 4.1 Instantaneous velocity Resource Uniform motion is simple to describe, but is rarely achieved in practice. Most objects do not move at a precisely constant velocity. If you drop an apple it will fall downwards, but it will pick up speed... 4.2 Instantaneous acceleration Resource The procedure of Question 15 for determining the instantaneous velocity of the car can be carried out for a whole set of different times and the resulting values of vx can be plotted against... 4.3 A note on functions and derivatives Resource This subsection introduces two crucially important mathematical ideas, functions and derivatives, both of which are used throughout physics. 4.4 Velocity and acceleration as derivatives Resource Recalling that the instantaneous velocity of a particle at time t is given by the gradient of its position–time graph at that time, we can now use the terminology of functions and derivatives to say that... 4.5 The signed area under a general velocity–time graph Resource We have already seen (in Section 3.6) that in the context of uniform motion, the signed area under a particle's velocity–time graph, between two given times, represents the change in the particle's position...

	5 Uniformly accelerated motion along a line 5.1 Describing uniformly accelerated motion Resource An important special case of non-uniform motion along a line is that which arises when an object is subjected to constant acceleration. This kind of motion is called uniformly accelerated motion. An object... 5.2 The equations of uniformly accelerated motion Resource Equations 22, 23 and 24 provide a complete description of uniformly accelerated motion. By combining them appropriately, it is possible to solve a wide class of problems concerning the kinematics of uniformly... 5.3 The acceleration due to gravity Resource In the absence of air resistance, an object falling freely under the influence of the Earth's gravity, close to the surface of the Earth, experiences an acceleration of about 9.81 m s−2 in the downward... 5.4 Drop-towers revisited Resource In Section 1 we described how research into near weightless conditions can be carried out on Earth by using a drop-tower or a drop-shaft (Figure 41). We are now in a position to examine drop-shafts in...

	6 Closing items 6.1 Unit summary Resource 1. A coordinate system provides a systematic means of specifying the position of a particle. A system in one dimension involves choosing an origin and a positive direction in which values of the position... 6.2 End-of-unit questions Resource Table 8 shows the atmospheric pressure P in pascals (Pa) at various heights h above the Earth's surface. Plot a graph to give a visual representation of the data in the table. Be careful to label...

	References and Acknowledgements Acknowledgements Resource