Derivation of Equation of Motion: Overview, Questions, Preparation

The equation of motion explains the concept of motion of an object. The derivations of the three equations of motion are crucial in kinematics. The equation of motion is defined as the equation that describes the behaviour of a physical system in terms of its motion as a function of time.

There are three equations of motion

1. First equation of motion- v = u + at
2. Second equation of motion- s = ut + 1/2(at2)
3. Third equation of motion- v2 = u2 + 2as

u is the initial velocity

v is the final velocity

t is the time

a is the acceleration

s is the displacement

= a = (v-u)/t

= v = u + at — (First equation of motion)

= Velocity = displacement / time

= displacement = velocity x time

Considering the velocity to not be constant, use average velocity in place of velocity.

= displacement = (u + v)/2 x t

= s = (u + v)/2 x t

Use the first equation in motion.

= s = {u + (u+at)}/2 x t

= s = (2u + at)/2 x t

= s = (2u/2 + at/2) x t

= s = (u + 1/2 x at) x t

= s = ut + 1/2(at2) — (Second law of equation)

= displacement = (u + v)/2 x t

= s = (u + v)/2 x t

From the first equation of motion, 

= v = u + at

= t = (v - u)/a

Replacing the value of ’t’ in the displacement equation

= s = (v + u/2) x (v - u/a)

= s = ( v2 - u2/2a)

= 2as = v2 - u2

= v2 = u2 + 2as — ( third equation of motion)

Derivation of Equation of Motion in Class 11

In the chapter, ‘Motion in a straight line’, you will be introduced to position, path length, displacement, average velocity and average speed, instantaneous velocity and speed, acceleration, kinematic equations, and relative velocity, and the derivation of the equation of motion.

1. In the following example of motion, what is the point object? 

A monkey sitting on top of a man cycling smoothly on a circular track

Ans- The monkey is smaller compared to the circular track. So, the monkey can be considered as the point object.

2. In the following example of motion, what is the point object? 

A railway carriage moving without jerks between two stations.

Ans- The carriage is smaller compared to the distance between the two stations. So, the carriage is considered as the point object.

3. In the following example of motion, what is the point object?

A tumbling beaker that has slipped off the edge of a table.

Ans- The size of the beaker can be compared with the height of the table. So, here nothing can be considered as a point object.

Q: What is an equation of a motion?

Q: What is the first equation of motion?

Q: What is the second equation of motion?

Q: What is the third equation of motion?

Q: Where does the derivation of equations play an important part?