# Physics Lesson 3.5.3 - What is Velocity? How do we measure it?

Welcome to our Physics lesson on What is Velocity? How do we measure it?, this is the third lesson of our suite of physics lessons covering the topic of Speed and Velocity in 1 Dimension, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

## What is Velocity? How do we measure it?

As discussed above, Speed is the Distance travelled in the unit of Time. But in the previous tutorials we have learned that there is another quantity besides Speed which is measured in the units of length. This quantity was called Displacement and its shows the change in position of an object. So, what happens is we divide Displacement by Time? Do we still get Speed?

The answer is NO. When dividing Displacement and Time, we obtain a new physical quantity known as Velocity.

Velocity is a vector quantity and it is denoted by v. Its formula is:

Velocity = Displacement/Time

In symbols,

v = ∆x/t

(In this instance we are discussing Speed and Velocity in one dimension, so Displacement is written as ∆x instead of ∆r).

Since Displacement is measured in metres and Time in seconds, the unit of Velocity is [m/s] just like the unit of Speed.

It is obvious Velocity is a vector quantity as it is obtained by dividing a vector by a scalar (look at the Physics tutorial Multiplication of a Vector by a Scalar).

### Example

An object moves uniformly for 20 seconds from A to C according the path shown in the figure.

Calculate:

1. Total Distance
2. Total Displacement
3. Speed
4. Velocity

of the object. Take π = 22/7.

### Solution

The object has moved in such a path that we have a half-circle and a straight line combined. For the half circle, we have:

sAB = s1 = 1/2 of Circumference
= 1/2 × 2 × π × r
= π × r
= 22/7 × 35 m
= 110 m

The Distance s2 is given; it is sBC = s2 = 80m.

Therefore, the total Distance s is:

s = s1 +s 2
= 110m + 80m
= 190m

Displacement (as the shortest path from A to C), represents the hypotenuse of the right triangle formed by the diameter of the half-circle AB and the line BC as shown in the figure.

Thus, since AB = d = 2r = 2 × 35 m = 70 m, we have for the Displacement (The length of the vector AC):

|AC|2 = |AB|2 + |BC|2
|AC|2 = (70m)2 + (80m)2
= 4900m2 + 6400m2
= 11300m2

Hence,

|∆x| = |AC| = √11300m2
≈ 106m

Now, it is easier to calculate the Speed. We simply divide the Distance found at (a) by the Time. Thus,

v = s/t
= 190m/20s
= 9.5 m/s

The same procedure is used to calculate the magnitude of Velocity, i.e. we will divide the Displacement found at (b) by the Time, t. Thus,

|v| = |∆x|/t
= 106m/20s
= 5.3 m/s

You have reach the end of Physics lesson 3.5.3 What is Velocity? How do we measure it?. There are 4 lessons in this physics tutorial covering Speed and Velocity in 1 Dimension, you can access all the lessons from this tutorial below.

## More Speed and Velocity in 1 Dimension Lessons and Learning Resources

Kinematics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
3.5Speed and Velocity in 1 Dimension
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
3.5.1What is Speed? How do we measure it?
3.5.2The meaning of Average and Instantaneous Speed
3.5.3What is Velocity? How do we measure it?
3.5.4Average and Instantaneous Velocity

## Whats next?

Enjoy the "What is Velocity? How do we measure it?" physics lesson? People who liked the "Speed and Velocity in 1 Dimension lesson found the following resources useful:

1. Definition Velocity Feedback. Helps other - Leave a rating for this definition velocity (see below)
2. Kinematics Physics tutorial: Speed and Velocity in 1 Dimension. Read the Speed and Velocity in 1 Dimension physics tutorial and build your physics knowledge of Kinematics
3. Kinematics Revision Notes: Speed and Velocity in 1 Dimension. Print the notes so you can revise the key points covered in the physics tutorial for Speed and Velocity in 1 Dimension
4. Kinematics Practice Questions: Speed and Velocity in 1 Dimension. Test and improve your knowledge of Speed and Velocity in 1 Dimension with example questins and answers
5. Check your calculations for Kinematics questions with our excellent Kinematics calculators which contain full equations and calculations clearly displayed line by line. See the Kinematics Calculators by iCalculator™ below.
6. Continuing learning kinematics - read our next physics tutorial: Speed and Velocity in 2 and 3 Dimensions