Question

Derive v²= u²+2aS by the graphical method , where v is the final velocity, u is the initial velocity, a is acceleration, and S the displacement

Answer 1

We will use both of the equations of motion to reach the third equation of motion. This will require a bit of algebra.

S=ut+  

2

1

​  

at  

2

andv=u+at, include the time variant t

There will be some situations when we do not have any information about time and so it would be a good idea to derive an equation that does not have a t term.

To do this, we rearrange our first equation to get  

t=  

a

v−u

​  

 

and use this to replace t wherever it appears in the second equation. So

S=ut+  

2

1

​  

at  

2

 becomes,

S=u(  

a

v−u

​  

)+  

2

1

​  

a(  

a

v−u

​  

)  

2

 

⇒2aS=2u(v−u)+(v−u)  

2

 

⇒2aS=2uv−2u  

2

−v  

2

−2uv−u  

2

 

⇒2aS=v  

2

−u  

2

 

⇒v  

2

=u  

2

+2aS.

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