Question

Derive the equation of motion for "position-time relation"​

Answer 1

Explanation:

Let us assume,

s = distance travelled      

t = time t

a = uniform acceleration

Therefore, Distance travelled by the object is given by area enclosed with OABC in the graph.

Therefore, s = area OABC ( Which is a trapezium )

= ( area of rect. OADC ) + ( Area of tri.ABD )

= ( OA × OC ) + 1/2 ( AD × BD )

NOW SUBSTITUTE :-

OA = u,

OC = AD = t

And

BD = at

We get :-

s = ut + 1/2 ( t × at )

∴ s = ut + 1/2 at²