(i) Consider a body which starts with initial velocity *u *and due to uniform acceleration *a*, its final velocity becomes *v *after time *t*. Then, its average velocity is given by

Average velocity = Initial\ velocity + Final\ velocity \over 2ย = ๐ข + ๐ฃ \over 2

โด The distance covered by the body in time *t *is given by

Distance, s = Average velocity x Time

orย {u + v \over 2} \times t*ย *or *s *= {u + (u + at) \over 2} \times t

โดย ย s = 2ut + at^2 \over 2ย ย ย orย s = ut + {1 \over 2} at^2

(ii) We know that,

s = ut + {1 \over 2} at^2

Also,ย ย a = v - u \over t

โนย ย ย t = {v - u \over a}

Putting the value of *t *in (1), we have

s = u({v - u \over a}) + {1 \over2}a({v - u \over a})^2

s = {uv - u^2 \over a} + {v^2 + u^2 - 2uv \over 2a}

2as = 2uv – 2u^{2} + v^{2} + u^{2} – 2uv

v^{2} – u^{2} = 2as