Hello dear students here we shall derive the equation of motion with detailed illustration. As we know that the motion can be explained in detail with parameters like velocity, acceleration, displacement and time. The first equation of motion gives the relation between the initial velocity, final velocity, acceleration and time.
So let’s derive it using the simplest method. i.e. graphical method.
Consider the body moving in XY plane starts its motion from point P with initial velocity ‘u’ (u ≠ 0) and reaches to point Q in time ‘t’ with uniform acceleration ‘a’and final velocity ‘v’ shown in figure below.
In graph X- axis represents time and Y-axis represents velocity,
From graph we have,
OP = u (initial velocity)
OQ’ = v (final velocity)
OS = t (time)
Draw QS perpendicular to X axis
Now draw PR ll OS
Then from graph, OS = PR, OP = SR and
OQ’ – OP = RQ = v – u = change in velocity
Acceleration is defined as the change in velocity per unit time, then from graph, slope of line PQ can also represents the acceleration,
This equation can be used to find initial velocity, final velocity, acceleration or time using the given data.
Let’s go through the following examples to discuss of first equation of motion.
Q.1. Boy cycling with initial speed of 6 m/s has uniform acceleration of 0.6 m/s2, what will be velocity of the boy in next 20 second?
Ans: Here we have, u= 6 m/s, a = 0.6 m/s2 and t = 20 s
then using first equation of motion, we have,
∴v=6+0.6×20
∴v=6+12
∴v=18 m/s
Q.2. Find the acceleration of car if its speed changes from 30 km/h to 60 km/hr in 15 sec?