Question

s= ut + 1/2 at square solve with graph

Answer 1

Hello Mate!

Area under V-T Graph shows displacement.

Are of trapezium = Area of triangle + Area of rectangle

s = l × b + 1/2 × b × h
s = t × u + 1/2 × t ( v - u )

Now as we know that at = v - u by 1st deriviation so, replace v- u by at

s = ut + 1/2 × t × at
s = ut +1/2 × at^2

Hope it helps☺!✌

Answer 2

Heya friend,



Here's your answer,



From the given figure,


We can find the distance travelled by the body in time t.


Distance travelled, S = Area under velocity-time graph (AB)


Or,


S = Area of trapezium OABD


  = Area of ΔABC + Area of rectangle OACD

  = 1/2 × Base × Height + Length × Breadth
  
  = 1/2 × AC × CB + OD × OA  ........................................... (1)


Here,

AC = OD = t

CB = DB - DC = (v - u)

OA = u



∴ Eqn (1) becomes,


S = 1/2 × t × (v - u) + u × t

   = ut + 1/2 (v - u) t  ......................................................(2)



We know,


v = u + at


Or,

(v - u) = at ............................. (3)




Put the values of eqn. (2) and eqn. (3),


We get,



S = ut + 1/2 at × t


Or,


S = ut + 1/2 at²


This equation is also known as position - timer relation.







Hope this helps!!!