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Derive the Third Equation of Motion: v2 – u2 = 2as
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The phenomenon of motion is when an item shifts positions. Displacement, distance, velocity, acceleration, speed, and time are all used to describe motion.
First Equation of Motion
The first equation of motion connects acceleration, time, and velocity.
v = u + at
This is the first equation of motion where,
a = acceleration
u = initial velocity
v = final velocity
t = time taken
Table of content
Second Equation of Motion
The second equation of motion connects time, displacement, velocity, and acceleration. The body’s displacement is depicted by the region underneath the v-t graph.
s = ut + ½ at2
Step 1: To prove:
v2 – u2 = 2as
Where
t is the time.
u is initial velocity,
v is final velocity,
a is the acceleration
and s is the displacement,
Step 2: Derivation:
We employ both of the equations of motion to obtain the third equation of motion.
s = ut + ½ at2 ….. (1) [Second equation of motion]
v = u + at …. (2) [First equation of motion]
On rearranging we get
t = (v – u)/a
Substitute the value of t in equation (1) s = ut + ½ at2
We get,
s = u (v – u)/a + ½ a (v-u/a)2
2as = 2u (v – u) + (v – u)2
2as = 2uv – 2u2 + v2 – 2uv + u2
On rearranging we get
2as = v2 – u2
v2 – u2 = 2as
Summary:-
Derive the Third Equation of Motion: v2 – u2 = 2as
The third equation of motion is v2 – u2 = 2as. It is an equation which connects the final velocity, initial velocity, acceleration and distance.
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