Question

V2=u2+2as
How can I prove that

Answer 1

Heya friend,
Here's the answer:

There are basically two ways to derive the equation:

1). By Graphical method(from velocity-time graph):

•(Refer the pic attached)

➡️The distance S travelled in time t= area of the traperzium OABD
Or. S=1/2 (OA+DB) × OD

Or. S=1/2 (u+v) × t..............(equation 1)

》We know that --> t=(v-u)/a

So, from eq. 1
》 S= 1/2(u+v)×[(v-u)/a] = 1/2[(v^2 -u^2)/a)
》 2 a S = v^2 -u^2
➡️Or v^2=u^2 +2as
Prooved.
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Now,
2).By Alternative Method:

Distance travelled=Average velocity× time

Or. S=(u+v)/2 ×t

》we know that (v=u+at)

t =(v-u)/a
S=(u+v)/2 × (v-u)/a = (v^2 - u^2)/2a

Or v^2 - u^2 =2aS

➡️v^2=u^2 +2aS
Hence, proved.
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Note : (^2 means square) !