Recalling that the instantaneous velocity of a particle at time t is given by the gradient of its positionâ€“time graph at that time, we can now use the terminology of functions and derivatives to say that the velocity of the particle is given by the derivative of its position function. In terms of symbols:

Author(s): The Open University

There is a simple feature of uniform velocityâ€“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 the velocityâ€“time graph and the change in position over a given time interval. Consider the following problem. A vehicle travels at a velocity vxÂ =Â 12Â mÂ sâˆ’1 for 4 s. By how much does its position change over that interval?

Author(s): The Open University

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 7, which shows the graph obtained by plotting the data in Table 2 and then drawing a smooth curve through the resulting points.

Author(s): The Open University

Video Materials

This extract is taken from S809 Â© 2005 The Open University.

All written material contained within this unit originated at the Open University.

Author(s): The Open University

The injection may be given immediately before the imaging process, or there may, for certain procedures, be a delay of several hours.

The patient's details and the dose being administered are carefully checked by two people before the injection is given. A lead-screened syringe is used to protect the staff from unnecessary radiation dose (see
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence. This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

T
Author(s): The Open University

During the twentieth century, astronomers extended their capabilities by developing telescopes and detectors that were sensitive to radio waves, microwaves, infrared and ultraviolet radiation, X-rays and gamma rays. All these forms of electromagnetic radiation, along with visible light, are emitted by the Sun.

Author(s): The Open University

You are about to meet some very large numbers, expressed in scientific notation, and some new units. The new units are those that are used to measure the amount of solar energy received by a part of the Earth's surface. Since plants are dependent on light for photosynthesis, the amount of plant material that ca
Author(s): The Open University

Wildebeest are only one of the species of plant predator that live in herds. Many others do too.

Activity 7

Watch the the TV programme from 30.48â€“47.32 and read LoM p. 109. Identify and write down (a) a couple of advantages and
Author(s): The Open University

You've seen plenty of evidence that reproduction in rodents â€“ more precisely what I've called their reproductive strategies â€“ are versatile and varied. You'll appreciate that â€˜versatile and variedâ€™ describes the range of sexual habits seen in the rodents as a group, not the behaviour within a single species. As DA says, some are monogamous, which means that individuals mate exclusively with one partner, over at least a single breeding cycle or season. The marmots are an example of a g
Author(s): The Open University

Radiation has energy and momentum, so we can use the molecules of a fluid such as air as an analogy for the photons of radiation. A detector pointing forwards along the direction of our motion (if any) will encounter a greater number of photons than a detector pointing backwards; in other words, it will record a higher intensity of 3 K radiation. (If the detector is tuned to a narrow band of frequencies one would also have to take account of the change in observed spectrum, but the principle
Author(s): The Open University

Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain

Author(s): The Open University

DDT is very effective in controlling pests, being very toxic to insects, and is cheap to produce. Its effectiveness is enhanced because it is very persistent, remaining active in the environment for a long time. This increases its value as an insecticide to farmers because one application lasts a long time, but is also a major reason why it poses a threat to wildlife and to human health. Although the agricultural use of DDT was banned in most developed countries 30 years ago, it can still be
Author(s): The Open University

Information is everywhere these days â€“ in the form of images, written records, tables and graphs. In this part of the unit we want you to realise how useful graphs can be to analyse numerical information, and to show you some techniques that can help you decide how reliable this numerical information is.

It's often difficult to spot a trend or a relationship in a long list of numbers. Because the human mind is highly adapted to recognising visual patterns, it is often much easier to u
Author(s): The Open University

An important point to remember when writing down measurements from a scale is never to quote more decimal places than you can reliably read from the measuring device you are using.

Author(s): The Open University

Unlike the Caledonian Orogenic Belt, outcrops of the Variscan Orogenic Belt are limited to the south-west of England, southern Wales and the south of Ireland (see Figure 9 and Author(s): The Open University

The following material acknowledged below is Proprietary and used under licence and not subject to Creative Commons licence (see terms and conditions).

Grateful acknowledgement is made to the following sources for permission:

Text

Rothery, David A., Teach Yourself Planets, Chapter 6, pp. 66â€“75, Hodder Education, 2000, 2003. Copyright Â© David Rothery.

Figures

Figures from
Author(s): The Open University

Activity 1: Elements and compounds

0 hours 10 minutes

Click on the video clip to watch Elements and Compounds, which focuses on water and its constituent elements.

Click below to v
Author(s): The Open University

The difficulty with having so much of the Earth's water locked up in the oceans is summed up poetically by Coleridge's â€˜Ancient Marinerâ€™, becalmed on board ship in the doldrums, beneath a blazing Sun.

Water, water, everywhere,

And all the boards did shrink;

Water, water, everywhere,

Nor any drop to drink.

(Samuel Taylor Coleridge, The Rime of the Ancient Mariner, 179
Author(s): The Open University

Let us now reconsider the sentence you heard in the imaginary scenario at the beginning of this unit. Here it is again.

• (1)Â Â My dad's tutor's no joker, and he told me the TMA's going to hit home with a bang.

Activity 2

Author(s): The Open University