# Velocity and Speed: Tutorials with Examples

Examples with explanations on the concepts of average speed and average velocity of moving object. More problems and their solutions can be found in this website.

## Average Speed and Average Velocity Definitions

The average speed is a scalar quantity (magnitude) that describes the rate of change (with the time) of the distance of a moving object.

 average speed = distance time

The average velocity is a vector quantity (magnitude and direction) that describes the rate of change (with the time) of the position of a moving object.

 average velocity = change in position time = displacement time

## Examples with Detailed Solutions

### Example 1:

An object moves from A to D along the red path as shown below in 41 minutes and 40 seconds.
a) Find the average speed of the object in m/s
b) Find the average velocity of the object in m/s Solution:
a) Using the given scale (1km per division); the total distance d is given by
d = AB + BC + CD = 2 + 5 + 2 = 9 km

 average speed = distance time = 9 km 41 mn + 40 s = 9000 m (41*60 + 40) s = 9000 m 2500 s = 3.6 m/s

b) The final and initial and positions of the moving object are used to find the displacement. The distance from A (initial position) to D (final position) is equal to AD = 5 km. The displacement is the vector AD whose magnitude if 5 km and its direction is to the east.

 average velocity = displacement time = 5 km 41 mn + 40 s = 5000 m 2500 s = 2.5 m/s

The average velocity is a vector whose magnitude is 2.5 m/s and its direction is to the east.

### Example 2:

An object moves, along a line, from point A to B to C and then back to B again as shown in the figure below in half an hour.
a) Find the average speed of the moving object in km/h.
b) Find the magnitude of the average velocity of the object in km/h. Solution:
a) The total distance d covered by the object is
d = AB + BC + CB = 5 km + 4 km + 4 km = 13 km

 average speed = distance time = 13 km 0.5 hour = 26 km/h
b) The magnitude of the displacement is equal to the distance from A (initial position) to B (final position) which is equal to 5 km.

 average velocity = displacement time = 5 km 0.5 hour = 10 km/h

### Example 3:

An fast object moves from point A to B to C to D and then back to A along the rectangle shown in the figure below in 5 seconds.
a) Find the average speed of the moving object in m/s.
b) Find the velocity of the object in m/s. Solution:
a) The total distance d is equal to the perimeter of the rectangle. Using the given scale,
d = 2 AB + 2 BC = 10 + 6 = 16 km

 average speed = distance time = 16 km 5 seconds = 16000 m 5 seconds = 3200 m/s
b) Since the moving object starts at point A and finish at A, there is no change in the position of the object and therefore the displacement is equal to zero.

 average velocity = displacement time = 0 5 second = 0

### Example 4:

A person walks, for two hours, from point A to B to C along a circular field as shown in the figure below.
a) Find the average speed of the person in km/h.
b) Find the velocity of the person. Solution:
a) The total distance d is equal to half the circumference of the circle and given by
d = (1/2)(2 * Pi * 3) = 3 Pi

 average speed = distance time = 3 Pi km 2 hours = 1.5 Pi km/h = 4.7 km/h

b) The magnitude of the displacement D is equal to the diameter AC of the circle and is given by
D = 2 * 3 = 6 Km with direction to the East

 average velocity = displacement time = 6 km 2 hours = 3 km/h

### Example 5:

A person walks for one hour and 12 minutes, from point A to point B, along a circular field as shown in the figure.
a) Find the average speed of the person in km/h.
b) Find the magnitude of the displacement of the person in km/h. Solution:
a) The total distance d is equal to the quarter the circumference of the circle and given by
d = (1/4)(2 * Pi * 3) = 1.5 Pi

 average speed = distance time = 1.5 Pi km 1 hour + 12 minutes = 1.5 Pi km 1 hour + 12/60 hour = 1.5 Pi km 1.2 hour

= 1.25 Pi km/h = 3.9 km/h
b) The magnitude of the displacement D is equal to the hypotenuse AB of the right angle ABO as shown below Use Pythagora's theorem to find AB as follows
AB
2 = 3 2 + 3 2 = 18
D = AB = 3√2 km

 average velocity = displacement time = 3√2 km 1 hour + 12 minutes = 3√2 km 1.2 hours

= 2.5√2 km/h = 3.5 km/h