[Physics Class Notes] on Speed And Velocity Pdf for Exam

We often find the terms speed and velocity as similar; however, practically, there’s a difference between them in terms of nature.

Let’s suppose I travelled 120 km in 5 hr, so obviously, my speed will be distance/time, i.e., 120/5 or 24 kmph. So this was the case for the speed, now if I ask which directions I took in my journey and from starting, in the middle, or while making turns and till the end, was my speed the same?  The answer will be clearly No; it’s because initially, the speed was 0 when my car was at rest when I started, it was slow, I also increased my speed, also decreased during the turns; on the whole, my speed wasn’t the same, which means I travelled with a velocity (varying speed) to cover 120 km distance in 5 hrs.

Overview of Speed and Velocity

Speed is defined as the distance travelled by an object in a unit of time. It doesn’t consider the direction of the object, i.e., it has only magnitude. This is how speed is called a scalar quantity. 

However, talking about velocity, velocity is defined as the rate of change of displacement. It is a vector quantity.

For example, I am planning to ride my vehicle on the hills of Himachal Pradesh at 65 kmph and on another trip, I plan to ride the same vehicle at 75 kmph in the West of Manali.

So, what difference do you find in both the trips?

Is it because of value or something else? Well! This page will help you acknowledge the difference in both the scenarios and also, why we consider speed and velocity as different parameters in Physics.

We often find the terms speed and velocity as similar; however, practically, there’s a difference between them in terms of nature. Here, we will look at some of the differences in speed and velocity in tabular form.

About Speed and its Types

Speed: According to Galileo, speed is defined as the distance covered per unit of time. For example, a man moving by car will cover a large distance as compared to a man moving by bicycle in the same time period. This is because a car can travel with more speed as compared to a bicycle. Speed is the magnitude part of the velocity in kinematics, thus it is a scalar quantity.

Speed = Distance/time

Its SI unit is metres per second. m/ s.

Instantaneous Speed: Instantaneous speed is the speed at any instant. For example, instantaneous speed can be seen on the speedometer of any vehicle. In mathematical terms, it is defined as the magnitude of the instantaneous velocity that is the derivative of the position concerning time. 

V=|v|= |dr/dt|

Average Speed: It is different from the instantaneous speed; average speed is the total distance travelled in a particular interval of time. In other words, the total covered distance divided by the total time interval is the average speed of the body.

  

Rotational Speed: It is a rotating speed. In other words, the rotational speed is the number of turns made by a body in unit time.

  

Tangential Speed: It is defined as the linear speed of a body travelling along a circular path. Mathematically, 

Tangential Speed= rotational speed x radial distance 

v = rω

Thus, tangential speed will be directly proportional to r when all parts of a system 

simultaneously have the same, as for a wheel, disk, or rigid wand.

Relative Speed: It is clear from its name that the speed of any body is relative to any other body that the speed of a body can be seen with reference to another body.

 

There are Two Types of Speed: 

Uniform Speed: When the distance travelled by a body is equal in equal interval of time then the speed is uniform. 

Non-uniform Speed: When the distance travelled by a body is unequal in an equal interval of time then the speed is known as non- uniform speed.

 

Velocity: Velocity is a physical vector quantity. It has a magnitude as well as direction. In calculus, velocity is the first derivative of the position with respect to time. Velocity, in other words, is the rate of change in the position of the body with reference to time. Its SI unit is metres per second. 

Velocity = displacement/time = (final position – initial position)/time

Relative Velocity: It is fundamental in both classical and physical physics. Relative velocity is a measurement of velocity between two objects as determined in a single coordinate system. 

Types of Velocity

Constant Velocity: A velocity that does not change with the direction and speed and moves along a straight line is called constant velocity.

 

Changing Velocity: A velocity that changes with the speed and direction or changes either speed or direction is called changing velocity. This is also called acceleration. 

Instant (Instantaneous) Velocity: When at a particular time, speed and direction change, then that phenomenon is called instantaneous velocity.

 

Terminal Velocity: When gravity takes over an object and results in the falling down of the object towards the earth through the atmosphere, then the constant velocity attained by the object is called terminal velocity.  

Differences Between Speed and Velocity

Now, let us understand the difference between speed and velocity in detail.

Speed vs Velocity

From the above text, we see that in velocity, we have a term called displacement. Displacement is the vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.

()

Here, we see that there are two directions from the initial to the final position, and we choose the shortest direction, which means the velocity at which the object moves makes velocity a vector quantity.

From our text, we understand that speed considers the magnitude, while velocity considers both magnitude and direction.

Distinguish Between Speed and Velocity

• Difference between distance and displacement- Distance, which is a scalar quantity deals with the total area covered by an object, whereas, a displacement which is a vector quantity deals with the change in the position of the object. The distance can never be zero, whereas, displacement can become zero)