Equations of Motion: First, Second, Third Equations and Applications

Equations of motion are very important rules in physics that tell us how an object moves when its speed changes at a constant rate. We see this in daily life when a car speeds up, a ball rolls down a slope, or a train slows down before stopping.

Have you ever noticed that when a bus starts, it slowly picks up speed instead of jumping instantly? That change in motion is explained using these equations.

Now the obvious question is, how do we describe motion using simple formulas? The fact is, physics gives us three main equations that connect speed, time, distance, and acceleration in a very clear way.

This article focuses on equations of motion, their meaning, and real-life applications in very simple language.

Table of Contents

• What is the Equation of Motion
• First Equation of Motion
• Second Equation of Motion
• Third Equation of Motion
• Real-Life Applications of the Equation of Motion

What is the Equation of Motion

Equations of motion are very important formulas in physics that describe how objects move when their speed changes at a constant rate. These equations help us understand how velocity, time, distance, and acceleration are connected in real-life motion.

Let’s first try to understand something interesting. When a car starts moving, it does not jump to full speed instantly. It slowly increases speed. This change in motion is explained using these equations.

Now the obvious question is, who introduced this idea?

In 1687, Sir Isaac Newton published his famous book Principia Mathematica, where he explained the laws of motion. These laws, along with mathematical expressions, helped people understand how objects move and interact in the physical world.

So, in simple words, equations of motion are mathematical formulas that describe how a physical system changes with time.

They help us calculate motion using basic quantities like:

• Velocity
• Time
• Acceleration
• Distance (displacement)

First Equation of Motion

The first equation of motion shows the relationship between initial velocity, final velocity, acceleration, and time. Mathematically, it can be represented as, 

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Now you may ask, what does this really tell us?

So, in simple words, this equation tells how velocity changes with time when acceleration is constant.

Have you ever noticed that a moving bicycle becomes faster when you pedal harder? That increase in speed is explained by this equation.

This is the most basic equation of motion and is used in almost every motion problem.

Second Equation of Motion

The second equation of motion explains the relationship between displacement, time, acceleration, and initial velocity.

s = ut + ½at²

Where s is displacement, u is initial velocity, a is acceleration, and t is time

Now there’s an interesting question: What does this formula really mean in real life?

So, in simple words, this equation tells us how far an object travels when it is moving with constant acceleration.

Let’s find out with examples,

• A car speeding up on a straight road
• A ball rolling down a slope
• A train with a gradually increasing speed

The fact is, this equation combines both the starting speed and the acceleration effect together.

Third Equation of Motion

The third equation of motion connects velocity, acceleration, and displacement without using time.

v² = u² + 2as

Where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

But how is this useful? This equation is very helpful when the time is not known in a problem.

For example,

• Falling objects under gravity
• Vehicle stopping distance
• Objects thrown upward

This equation gives a direct relation between speed and distance.

Real-Life Applications of Equations of Motion

Equations of motion have many uses in our daily lives and in different fields of science and engineering. These equations help us calculate unknown quantities of motion when some information is already given.

Let’s find out some important applications of equations of motion.

• Finding the Distance Travelled: If the initial velocity, final velocity, and acceleration of an object are known, we can calculate the distance travelled even if the time is not given.
• Finding the Time of Motion: We can determine the time taken by an object to move if we know its initial velocity, final velocity, and acceleration.
• Finding the Displacement Without Final Velocity: Sometimes, we know the initial velocity, acceleration, and time, but the final velocity is not known. In such cases, equations of motion help us calculate the distance travelled.
• Finding the Initial Velocity: Equations of motion can also be used to calculate the starting speed of an object when the final velocity, acceleration, and time are known.
• Finding the Final Velocity: If the initial velocity and acceleration are known, we can easily calculate the final velocity of an object after a certain time.
• Solving Real-Life Motion Problems: Interestingly, these equations are widely used in many real-world situations, such as
• Designing vehicles and roads
• Studying the motion of rockets and satellites
• Calculating the braking distance of vehicles
• Analysing the movement of athletes in sports
• Studying falling objects under gravity

Till now, we learned that the first equation of motion helps find the change in velocity, the second equation calculates displacement, and the third equation of motion is useful when time is not known. We also saw how these equations are used in real-life situations such as moving vehicles, sports, and falling objects.