define the expression
[tex]s = ut + \frac{1}{2} {at}^{2} [/tex]
in Mathematical and in graphical​

2 thoughts on “define the expression<br />[tex]s = ut + \frac{1}{2} {at}^{2} [/tex]<br />in Mathematical and in graphical​”

1. Answer:

   Velocity is defined as the rate of change of displacement. This is mathematically represented as:

   Velocity=DisplacementTime

   Rearranging, we get

   Displacement=Velcoity×Time

   If the velocity is not constant then in the above equation we can use average velocity in the place of velocity and rewrite the equation as follows:

   Displacement=(InitialVelocity+FinalVelocity2)×Time

   Substituting the above equations with the notations used in the derivation of the first equation of motion, we get

   s=u+v2×t

   From the first equation of motion, we know that v = u + at. Putting this value of v in the above equation, we get

   s=u+(u+at))2×t

   s=2u+at2×t

   s=(2u2+at2)×t

   s=(u+12at)×t

   On further simplification, the equation becomes:

   s=ut+12at2

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2. Answer:

   Derivation of Second Equation of Motion by Graphical Method

   From the graph above, we can say that

   Distance travelled (s) = Area of figure OABC = Area of rectangle OADC + Area of triangle ABD

   s=(½AB×BD)+(OA×OC)

   Since BD = EA, the above equation becomes

   s=(½AB×EA)+(u×t)

   As EA = at, the equation becomes

   s=½×at×t+ut

   On further simplification, the equation becomes

   s=ut+½at²

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