Question

Derive fourth equation of motion by algebraic method?

Answer 1

Derivation of fourth equation of motion

To derive the fourth equation of motion, first we have to consider the equation for acceleration and then to rearrange it.

Acceleration a = (v-u) /t

Or at = (v-u)

Or t = (v-u) /a

Next step is to substitute the equation for the time t into the second equation of motion s=ut + at2/2   to obtain:

s = u[(v-u)/a]  + a [(v-u)/a]2 /2  

or s = u(v-u)/a  + (v-u)2 /2a

or s =[2u+v-u](v-u)/2a

or  s = (u+v)(v-u)/2a = (v+u)(v-u)/2a

or  s= (v2-u2)/2a  

or  2as = v2 –u2

or v2 –u2  =   2as    

or v2 = u2 + 2as     and this equation of motion can be used to find the final velocity or the distance travelled if the other values are given.

Answer 2

Explanation:

In the same manner fourth equation of motion[S = vt – ½ at2] and fifth equation of motion [S = ½ (u + v) × t] is also derived from velocity-time graph. Hence, the total equations of motion are five.