## Motion along a line

Strange to think but a very common idea in physics is the idea of a **particle. **A point like concentration of matter that has no size, no shape, and no internal structure: A singularity! 🙂

The branch of physics concerned with the description of motion is known as **Kinematics**. It is not concerned with forces, nor with the causes of motion.

Its concerns are:

- Where is the particle
- How fast is it moving and in what direction.
- How rapidly is it speeding up or slowing down

Easiest to describe with a graph of Position against time: e.g. For:

Time/t |
Position/m |

1 | 1 |

2 | 4 |

3 | 9 |

4 | 16 |

5 | 25 |

(Yes, I know the graph doesn’t have any labels and it really should, but have you ever tried using Word to create a graph!?) Anyway. . . Position/m along the vertical axis, and Time/s along the horizontal. (Even worse… You ever tried copying a Word graph to HTML and a Blog!!?)

The above graph represents the position of a particle whose velocity is changing with time, it’s speeding up, accelerating. If the speed was constant you’d see the graph below

Time/t |
Position/m |

1 | 2 |

2 | 4 |

3 | 6 |

4 | 8 |

5 | 10 |

Again: Position/m along the vertical axis, and Time/s along the horizontal.

This constant speed is known as Uniform Motion and as you can see it creates a straight line graph.

The general form of equation for a straight line is:

S=At + B, where A and B are constants. B being the intercept (where the sloping line crosses the vertical axis) and A being the slope (the steepness of the line), t is the value along the vertical axis (which in this case is time/t).

**Velocity** is defined as the rate of change of position with respect to time, i.e.

(change of position)/(change in time) = (*x*2-*x*1)/(*t*2-*t*1), sometimes referred to as the ‘rise over the run’

**Speed** and velocity are not the same. Velocity has a direction whereas speed is just a value. It is the magnitude of the velocity, i.e, the value of the velocity irrespective of its sign (or direction), often written as |*v*|

In graphical terms, the velocity Δ*s*/Δ*t* is the slope of the particle’s position-time graph, the steepness of line representing the particles speed.

The initial position of the particle (i.e. where it was at time, t = 0), is where the line crosses the vertical axis, known as the **intercept**.

From the equation of a straight line graph it is easy to see that the **Uniform Motion Equation** is:

*x* = *v _{x}t *+

*x*

_{0}*v _{x}* = constant

and the **displacement** between two point, *s* = (*x _{2}-x_{1}*)

*s _{x}* =

*v*

_{x}t