Question

derive graphically the equation for postion time relation for an object travelling s and in time t under uniform accelecration

Answer 1

The graph represents the motion of the object is under constant acceleration.
here, u=AO=CD ≠ 0
Now see that,
distance, x = v•t
therefore the total area under the acceleration of velocity time graph will give the distance covered.
therefore,
distance, x = ar(OADC)+ar(∆ABD)
= OA•OC+ ½(AD•BD).............(1)
Now, OA = u
OC = t
AD = t (same as above t)
BD = v – u = a•t (by first equation of motion)
substituting the values in ..(1),
x = u•t + ½ (t)•(a•t)
so,
$distance \: \: x = ut + \frac{1}{2}a {t}^{2}$