Derivation of Second Equation of Motion


 
 
Concept Explanation
 

Derivation of Second Equation of Motion

Derivation Of Second Equation Of Motion: This equation is also known as Equation for Position-Time Relation (Second Equation)

Let us suppose that an object has travelled a distance s in time t under uniform acceleration a.

From the given figure, the distance travelled by an object is obtained by the area enclosed within OABD under the velocity-time graph AB.

Thus, the distance s travelled by the object is given by

   s = area of OABD          [ Which is a trapezium ]

      = area of the rectangle OACD + area of the triangle ABC

      =OAtimes OD+frac{1}{2}(ACtimes BC)                   ........(iv)

But  OA = u, OD = AC = t, BC = at

Substituting the above values in Eq. (iv), we get

large s=utimes t+frac{1}{2}(ttimes at)  

    large s=ut+frac{1}{2}at^{2}

Hence, the second equation of motion has been derived.

 

Sample Questions
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Question : 1

The breaks applied to a sooter produces a retardation of 6m/s^2.if the sooter takes 2 seconds to stop after applying the breaks,the distance it covers during this time is-

Right Option : A
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