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Chapter Contents

• Kinematics
• 1. Velocity (s-t) Graphs
• 2. Acceleration (v-t) Graphs
• 3. Kinematics Exercises

• Comments, Questions?

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1. Velocity (s-t) Graphs

Example 1:

This general graph represents the motion of a body travelling at constant velocity. The graph is linear (that is, a straight line).

Recall that linear equations have the general form

y = mx (m is a constant and x is a variable).

The number m is called the slope of the line ().

In the above graph, we have the function:

displacement = velocity × time

or

s = v × t

Velocity is constant and time is a variable.

We note that the graph passes through (0,0) and has slope v. The slope of the line tells us the velocity. We can also write the velocity using delta notation:
which means "change in displacement over change in time".

If we have a high velocity, the graph has a steep slope. If we have a low velocity the graph has a shallow slope (assuming the vertical and horizontal scale of each graph is the same).

High speed Low speed

Example 2

A marathon runner runs at a constant 12 km/h.

a. Express her displacement travelled as a function of time.

b. Graph the motion for 0 ≤ t ≤ 4 h

Answer

Displacement-time Graphs

Example 1

This is the graph of a journey by sports car:

a. What is the velocity for each stage of the journey?

b. What is the average (mean) velocity for the whole journey?

Answer

Example 2

A particle in a magnetic field moves as follows:

Find the velocity for each part of the motion.

Answer