​ Derive s = ut + 1/2 at^2 Derive one equation for displacement of a body which is in the uniform acceleration. ​

Question

Derive s = ut + \(\frac{1}{2}\)at² Derive one equation for displacement of a body which is in the uniform acceleration.

Answer 1

1) Let u be the initial velocity, 

v be the velocity at time ‘t’. 

a be the acceleration,

s be the displacement

2)     

3) The body is in the uniform velocity ,acceleration is constant.

Average velocity = \(\frac{v\,+\,u}{2}\)      ------------(1)

4)  Also we know average velocity = \(\frac{s}{t}\)     --------------- (2)

5) From (1) and (2)  \(\Rightarrow \)\(\frac{v\,+\,u}{2}=\frac{s}{t}\)     

6) We know that u + at= v         ----------------(3)

Substitute (3) in 

\(\frac{v\,+\,u}{2}=\frac{s}{t}\Rightarrow\frac{u\,+\,at\,+\,u}{2}=\frac{s}{t}\Rightarrow\frac{2u\,+\,at}{2}=\frac{s}{t}\Rightarrow ut \,+\, \frac{1}{2}at^2=s\)

7) s = ut + \(\frac{1}{2}\)at²