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obtain equations of motion for constant acceleration using method of calculus |
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Answer» Thabkyou she is the best.. Let uniform acceleration be aAcceleration is defined as rate of change of velocity ......................(1)where v is velocity of an object at time tBy integrating above ewqn.(1) , we getwhere u is velocity at time t = 0 and v is velocity after time t secondsfrom above integration we get , v - u = a t or v = u + ( a t ) ...................... (2)velocity is defined as rate of change of displacement\xa0\xa0...................(3)Where S is distance travelled.By integrating above equation (2) , we getWhere xo\xa0is initial position and x is position after time tx - xo\xa0= u t + (1/2) a t2\xa0.................. (4)If the object travelled a distance S staring from initial velocity u and attained final velocity v after travelling distance S in time t , then we haveS = (1/2) ( u+v ) t ...............(5)Let us substitute t from eqn.(2) in eqn.(5) as t = [ ( v - u ) / a ] , then we haveS = (1/2) ( u + v ) [ ( v - u ) /a ] or v2\xa0= u2\xa0+ ( 2 a S ) .................. (6)Eqn.(2) , eqn.(4) and eqn.(6) are equations of motion |
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