3.3 Initial position and the intercept of the position-time graph
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 particular time?' The most common way of answering this question is to specify the initial position of the particle, that is, its position at time t = 0 s.
Although it is common to refer to the position at t = 0 as the 'initial position' it is also possible, and sometimes more convenient, to associate the initial position with some other time.
The initial position of a uniformly moving particle is easily determined from its position-time graph. It's just the value of x when t = 0, i.e. the value of x at which the straight line crosses the vertical axis through the origin. In Figure 12a, for example, it is x = −20 m. This value is generally referred to as the intercept.
One point to bear in mind though; it is sometimes advantageous to draw position-time graphs that do not include the origin (for instance, you might be asked to draw a graph for the period from t = 100 s to t = 110 s). When dealing with such graphs do not make the mistake of thinking that the value at which the line crosses the vertical axis is the intercept. You can only read the intercept directly from the graph if the vertical axis passes through the zero value on the horizontal axis.
A little thought should convince you that the gradient and the intercept of a straight line entirely determine that line. In the same way, the velocity and the initial position of a uniformly moving particle entirely determine the motion of that particle. In the next subsection you will learn how these graphical and physical statements can be represented algebraically, in terms of equations.