# Linear Acceleration

Introduction

This topic is about particles which move in a straight line and accelerate uniformly. Problems can vary enormously, so you have to have your wits about you. Problems can be broken down into three main categories: Constant uniform acceleration

Time-speed graphs

Problems involving two particles

Constant uniform acceleration

Remember what the following variables represent: t = the time ; a = the acceleration ; u = the initial speed ; v = the final speed ; s = the displacement from where the particle started. When the acceleration is negative, it is sometimes called a deceleration or retardation. For example, an acceleration of –3 ms-2 is the same as a deceleration (or retardation) of 3 ms-2. • To answer this question, you will need to use the four key formulae intelligently. They are: • It is important to know the second of these equations off by heart; the others appear on Page 40 of The Mathematical Tables. Secondly, you may be asked to derive either of the last two equations from the first two. Practise this.

• These four formulae will be useful elsewhere (for example when doing Questions 3 and 4 on projectiles and connected particles).

Time-speed graphs

Remember that the above formulae may be used only while the acceleration is uniform. If a particle speeds up, but then travels at a constant speed, and then slows down, the above formulae cannot be used for the entire journey. In these cases we solve the problem by drawing a time-speed graph, with time as the horizontal axis. There are four key points to remember about time-speed graphs: • The area between the graph and the time-axis represents the distance travelled.

• The slope of the graph represents the acceleration.

• If a particle starts from rest, then v = at [i.e. the final speed will be the product of the acceleration and the time.]

• If a particle accelerates from rest for...

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