0.2 Motion in one dimension  (Page 4/16)

The differences between distance and displacement can be summarised as:

Point of reference

1. Use [link] to answer the following questions.
   1. Jill walks to Joan's house and then to school, what is her distance and displacement?
   2. John walks to Joan's house and then to school, what is his distance and displacement?
   3. Jack walks to the shop and then to school, what is his distance and displacement?
   4. What reference point did you use for each of the above questions?
2. You stand at the front door of your house (displacement, $\Delta x=0\mathrm{m}$ ). The street is $10\mathrm{m}$ away from the front door. You walk to the street and back again.
   1. What is the distance you have walked?
   2. What is your final displacement?
   3. Is displacement a vector or a scalar? Give a reason for your answer.

Speed, average velocity and instantaneous velocity

Velocity

Velocity is the rate of change of displacement.

Instantaneous velocity

Instantaneous velocity is the velocity of a body at a specific instant in time.

Average velocity

Average velocity is the total displacement of a body over a time interval.

Velocity is the rate of change of position. It tells us how much an object's position changes in time. This is the same as the displacement divided by the time taken. Since displacement is a vector and time taken is a scalar, velocity is also a vector. We use the symbol $v$ for velocity. If we have a displacement of $\Delta x$ and a time taken of $\Delta t$ , $v$ is then defined as:

Velocity can be positive or negative. Positive values of velocity mean that the object is moving away from the reference point or origin and negative values mean that the object is moving towards the reference point or origin.

Average velocity (symbol $v$ ) is the displacement for the whole motion divided by the time taken for the whole motion. Instantaneous velocity is the velocity at a specific instant in time.

This is terminology that occurs quite often and it is important to always remember that instantaneous and average quantities are not always the same. In fact, they can be very different. The magnitude of the instantaneous velocity is the same as the slope of the line which is a tangent to the displacement curve at the time of measurement. The magnitude of the average velocity is the same as the slope of the line between the start and end points of the interval.

If you want to think about why the tangent at a particular time gives us the velocity remember that the velocity is the slope of the displacement curve. Now, a simple why to start thinking about it is to image you could zoom (magnify) the displacement curve at the point. The more you zoom in the more it will look like a straight line at the point and that straight line will be very similar to the tangent line at the point. This isn't a mathematical proof but you will learn one later on in mathematics about limits and slopes.