Question

derive the two equations of motion

Answer 1

The three equations of motionv = u + at ; s = ut + (1/2) at2 and v2 = u2 + 2as can be derivedwith the help of graphs as described below. Consider the velocity – time graph of a body shown in the below Figure.Velocity–Time graph toderive the equations of motion.

Answer 2

1.First Equation of Motion-:We know ,acceleration (a) =[math]\dfrac {Change\:in\:velocity} {Time\:taken} [/math]a=[math]\dfrac {Final\:velocity-Initial\:velocity} {Time\:taken} [/math]or => a=[math]\dfrac {(v-u)} {t}[/math]or => at= v-uor => v= u+ at —————(i)



2. Second Equation ofMotion -:We know ,=> Distance travelled= Average Velocity × Time=> Distance travelled=[math]\dfrac{Initial\:Velocity + Final\:Velocity} {2 }\times Time[/math]=> s=[math]\dfrac {v+u} {2} \times t[/math]From equation (i) => v=u+at∴ s =[math]\dfrac {u+(u+at)}{2}\times t[/math]or s =[math]\dfrac { (2u+at)} {2}\times t[/math]or s= ut + (1/2 • at²) —————(ii)

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