Speed Formula

In the world of physics, time, speed, distance, displacement and velocity are some of the fundamental physical quantities that govern the motion of an object. Understanding these fundamentals of physics are necessary for students to build a strong base in physics. As a part of introductory physics courses, students learn about various physics formulas and their wide applications in daily life.

What is Speed in Physics?
Speed thrills many of us especially when we wish to have some fun riding our bikes or go for long drives. Ever wondered how physics defines speed? Well, we all know that a fast-moving car can cover some specific distance in a relatively short period while a less speed car takes a longer time. So speed is linked to two basic parameters - time and distance. In other words, speed is a function of time and distance. The more the speed, the faster you reach your destination. So, this description must have given you some idea about how to define speed. Well, simply stated, speed is the rate at which an object is moving. Now the term "rate" refers to the factor per unit time. Speed is defined as "distance traveled per unit time".

This forms a very elementary definition of speed. However, for physics students, a crucial factor that is of paramount importance must be considered while defining speed. A very closely related physical quantity velocity is often confused with speed. So how are speed and velocity different? Students of physics must be aware of scalar and vector quantities. Quantities that have specific direction and magnitude are known as vector quantities while those representing only magnitude are called scalar quantities. Speed is a scalar quantity while velocity is a vector quantity. Speed represents the magnitude of velocity. When you state the speed of an object, you can say, for instance 55 km/hr. However, when you state the velocity, you have to say that it is 55 km/hr east or any other direction. Direction is an important parameter for velocity. The direction of velocity is the direction in which the object moves and it is represented by a vector sign.

Formula for Speed
Now that we have discussed the definition of speed, let's now discuss the formula for it. The speed of an object that travels a distance (d) over a period of time (t) is given by:

Speed (V) = Total Distance Traveled / Total Time Taken = d/t

Students with basic knowledge of calculus can also understand the instantaneous and average formula for speed. Instantaneous speed is the speed at a particular moment of time.

Instantaneous Speed Formula = dS/dT, where 'S' is the distance covered and 'T' is the time taken.

Generally, during traveling and motion, speed is not constant throughout the journey. Instead speed tends to decrease or increase depending on various factors. In such cases, instead of speed, average speed is measured as that gives an average value of the speed for the entire journey.

Speed Equations
In the field of one dimensional motion or kinematics, following speed equations are very commonly used. Let 'u' and 'v' be the initial and final speed of an object, 'S' the distance covered in time 't', then the speed equations are given by:

• v = u + at
• v² = u² + 2aS
• S = ut + 1/2at²

Angular Speed Formula

As students learn more about motion equations and mechanics, they will also gain knowledge about rotatory motion. Just like linear speed is concerned with one dimensional motion, angular speed is related to circular motion. The formula for angular speed is given by:

v = ωr, where v is linear speed, ω is angular speed and r is the radius of circle.

No quantity in physics is complete without its unit. According to the SI system, the standard unit for measuring speed is meters per second i.e. m/s. Depending on the units used for distance and time in speed formula, we can get various units of speed. Speed equations are basic concepts in physics and trying to understand their derivation and use can go a long way in giving you a strong background in physics.