Average speed and instantaneous speed are both concerned with the rate with which distance is traveled. Both are calculated by dividing a distance traveled by the time involved. The essential difference between these two quantities is in the method of determining which distance and which time to use.

In the case of average speed, the total distance and the total time are used for the calculation. To determine the instantaneous speed, you choose a small time interval during which the speed is constant. As a practical example, in your automobile you determine the average speed for a trip by taking the distance traveled as indicated by the odometer and dividing by the elapsed time, e.g. you travel a distance of 180 miles in 3.5 hours for an average speed of 51.4 miles per hour. You determine the instantaneous speed by reading the speedometer, which uses a device to continuously measure the speed. Essentially the speedometer measures the distance traveled during a very short time. The calculation of the average speed provides no information about variations in speed during a trip. The calculation of instantaneous speed assumes that the speed was held constant during the short time interval of the calculation, e.g. during the time interval in which your car's speedometer makes a measurement.

Vectors are used to represent quantities that must be specified by reporting both the magnitude (how large the vector is) and the direction in which the action occurs. A vector provides a convenient way in which to keep track of both magnitude and direction. Examples of physical quantities that are represented as vectors are: velocity, acceleration, force, momentum, electric field strength, and magnetic field strength.

Scalar quantities are completely specified by giving the magnitude only. Examples of scalars are: mass, time, volume, temperature, and speed.

Velocity differs from speed in that velocity includes information about the direction of motion. The speed of an automobile might be specified as 50 miles per hour, i.e. a scalar with magnitude only, while the velocity of that same automobile might be described as 50 miles per hour heading due east. Note that the specification of the velocity involves both magnitude and direction.

Acceleration deals with a change in velocity. That change could be a change in the magnitude of the velocity or a change in the direction of the velocity or a change in both magnitude and direction of the velocity. The magnitude of the acceleration is calculated by finding the change in the magnitude of the velocity and dividing it by the time required to produce that change.

A graph provides a visual presentation of how one quantity varies with respect to another. It is often possible to gain insight into the motion of an object by simply glancing at a graph of distance-versus-time or of velocity-versus-time. The slope of the distance-versus-time curve at any point on the graph is equal to the instantaneous velocity of the object at that time. A large upward slope on a distance-versus-time graph represents a large positive instantaneous velocity, i.e. an instantaneous velocity in the forward direction. A zero slope or horizontal line represents a zero velocity. A downward slope represents a negative instantaneous velocity or a velocity in the backward direction.

The instantaneous acceleration is equal to the slope of the velocity-versus-time graph. A steep slope represents a rapid change in velocity and thus a large acceleration, while a horizontal line has zero slope, and therefore represents a zero acceleration.

The distance traveled is equal to the area under the velocity-versus-time graph. When the velocity is negative, which is represented on the graph by a line below the time axis on the graph, the object is traveling backwards and its distance from the starting point is decreasing with time.

The case of uniform acceleration occurs often in physics. If the acceleration is constant, the velocity changes uniformly with time and the graph of velocity versus time is a straight line. The distance traveled in the case of uniformly accelerated motion varies with the square of the time.