Question

fourth equation of motion

Answer 1

v= u + at 

s =( u + v ) t /2 

s = ut + at2/2

v2 = u2 + 2as 

Derivation of Newton's Equations of Motion:Derivation of First and second equations of motion:We know that,Velocity is the Change in displacement / Change in time,v = ds/dt = s/t andAcceleration is the change in velocity / change in time,a = dv/dt = (v-u)/tOr the acceleration is the change in speed per unit time,
therefore,a = (v-u) /tor at = v-uor v= u + at and it is the first Equation of Motion


Derivation of third and Fourth Equations of Motion:Derivation of third equation of motionThe third equation of motion can be derived by substituting the value of v from the first equation into the second equation.First equation is v= u +atAnd the second equation is s = (u+v)t /2 Or s=[u + (u+at)] t /2 =[2u+at]t /2 = [2ut+ at2] / 2 =ut + at2/2Or s=ut + at2/2 and this is the third equation of motion.


Derivation of fourth equation of motionTo derive the fourth equation of motion, first we have to consider the equation for acceleration and then to rearrange it.Acceleration a = (v-u) /tOr at = (v-u)Or t = (v-u) /a