Question

derive v=u+at from s=ut +1/2at²​

Answer 1

Answer:

At t = 0, initial velocity = u = OA

At t = t, final velocity = v = OC

The distance S travelled in time t = area of the trapezium OABD

s = (1/2) x (OA + DB) × OD

s = (1/2) x (u + v) × t

Since v = u + at,

s = (1/2) x (u + u + at) × t

s = ut + (1/2) at2

Answer 2

Explanation:

1. v = u + at :-

a= acceleration

v=initial velocity

u= final velocity

time =t

a=change in velocity / time

=>a=v-u/t

=> a=v-u/t

=>at=v-u

=>v=u+at

2. s=ut+1\2at ^2

s=displacement

u=initial velocity

t=time

a=acceleration

average velocity =v+u/2 = s/t-------(1)

=> s= (v+u/2)×t { (v+u/2)from equation 1 }

s=[u+at+u/2]×t

s=2ut+at^2/2

《s=ut+1/2at^2》