please derive the equation v*v=u*u+2as  for me i am really confused

Asked by meghana.omprakash | 29th Oct, 2015, 09:33: PM

Expert Answer:

Consider the velocity–time graph of a body with initial velocity ‘u’ at point A.
 
It has uniform acceleration from A to B because its velocity changes uniformly in time ‘t’. After time t, its final velocity is ‘v’.
 In the graph, u = OA, v = CB, t = OC.
We draw perpendicular CB from point C and draw AD parallel to OC. Also, BE is the perpendicular from B to OE.
 
Third equation of motion: v= u+ 2as
The distance travelled is equal to the area of the figure OABC. Now, OABC is a trapezium.
begin mathsize 14px style Distance space travelled equals straight s equals Area space of space trapezium space OABC space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half cross times left parenthesis sum space space of space parallel space sides right parenthesis cross times height space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 1 half left parenthesis OA plus BC right parenthesis cross times straight O Now comma space we space have space space space and space space. space Thus comma space the space distance space travelled space is straight s equals 1 half cross times left parenthesis straight u plus straight v right parenthesis cross times straight t space space space space space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis Eliminate space ‘ straight t ’ space from space the space above space equation space with space the space help space of space the space first space equation space of space motion space as straight v equals straight u plus at space space space space space space at equals straight v minus straight u straight t equals fraction numerator straight v minus straight u over denominator straight a end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... space left parenthesis 2 right parenthesis Substitute space equation space left parenthesis 2 right parenthesis space in space equation space left parenthesis 1 right parenthesis straight s equals fraction numerator left parenthesis straight u plus straight v right parenthesis left parenthesis straight v minus straight u right parenthesis over denominator 2 straight a end fraction therefore 2 as equals straight v squared minus straight u squared therefore straight v squared equals straight u squared plus 2 as Thus comma space the space third space equation space is space straight v squared equals straight u squared plus 2 as. end style

Answered by Faiza Lambe | 30th Oct, 2015, 08:30: AM