Question

drive graphically the equation for position time relation for an object travelling a distance 's' in time 't' under uniform acceleration.

Answer 1

see pic, Let a body moves from D to with initial speed u and are moving with uniform acceleration finally body reach point B after time taken t.

distance travelled by body = area between curve v-t
= area DBA + area DAEO
= 1/2 × base × height + length × Breadth
= 1/2 × t × (v - u) + ut

we know , ( v - u ) = at, put it above

= 1/2× t × at + ut
= ut + at²/2

hence , distance travelled by body = ut + 1/2at²

Answer 2

S=Area OABC [which is trapezium]

=area of the rectangle OADC+area of the triangle ABD

=[OA×OC]+[1/2(AD×BD)]

=[u×t]+[1/2(t×at)]

=it+1/2at×t

so

S=it+1/2a×t×t