Social Sciences, asked by priyachand8691shines, 9 months ago

Derive expression for kinetic energy...

Answers

Answered by sonysneha146
1

hey mate here is your answer...

Derivation for the equation of Kinetic Energy:

The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is 

                           v2 - u2 = 2aS

This gives

 

                          S = ½a(v2 - u2) 

                          S = ½a(v2 - u2)

 We know F = ma. Thus using above equations, we can write the workdone by the force, F as

                          S = ½a(v2 - u2)

 We know F = ma.

Thus using above equations, we can write the workdone by the force, F as                 W = ma × ½a(v2 - u2) 

                 S = ½a(v2 - u2)

                               or                              W=m( v 2 - u 2 ) ½

 If object is starting from its stationary position, that is, u = 0, then

                          S = ½a(v2 - u2) 

We know F = ma. Thus using above equations, we can write the workdone by the force, F as                            W = ma × ½a(v2 - u2)                                   or                             W =m( v 2 - u 2 ) ½If object is starting from its stationary position, that is, u = 0,

then                            W = ½mv2

                                                                      or                 W =m( v 2 - u 2 ) ½

If object is starting from its stationary position, that is, u = 0, then                     

                          S = ½a(v2 - u2)                     

It is clear that the work done is equal to the change in the kinetic energy of an object.If u = 0, the work done will be  W = ½mv2Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek=  ½mv2

hope this answer helps you..

Answered by thapaavinitika6765
2

Expression for Kinetic energy(Ek)-

Consider an object with mass m, moving with initial velocity u.

Let a force F, act on it causing a displacement s, along the direction of force and accelaration.

Let the object attain final velocity v. We know

F = m x a ------------------------ 1

By position velocity relation we have, V2 = u2 + 2as or s = v2 -u2 2a----------------------------- 2

The work done by the force W = F x s -------------------------------------- 3

Substituting 1 and 2 in 3

W = (m x a) x (v2 - u2/2a) W = m/2 (v2 - u2) W = 1/2 mv2 - 1/2 mu2 -------------------- 4

For an object to be at rest in the beggining, u = 0

Therefore, W = 1/2 mv2 W = Ek ( Ek = kinetic energy)

Therefore, Ek = 1/2 mv2

Similar questions