Question

Derive the expression for kinetic energy of an object starting from rest.​

Answer 1

Answer:

Expression for Kinetic Energy:

Explanation:

Suppose a stationary object of mass m moves because of an applied force. Let u be its initial velocity  [here u=0]. Let the aplied force be F. This generates an acceleration a in the object and, after time t, the velocity of the object becomes equal to v. The displacement during this time is s. The work done on the object, W= F.s [Force x displacement]

According to Newton's second law of motion,

F= ma ___ (1) [similarly using Newton's second equation of

                       motion. However, as u=0]

s= ut + 1/2 at^2

s= 0 + 1/2 at^2

s= 1/2 at^2 ___ (2)

Therefore, W= ma x 1/2 at^2 ___[ using equations (1) and (2)]

                      W= 1/2 m(at)^2  { a is two times so a^2} ___(3)

Using Newton's first equation of motion,

v= u +at

v= 0 + at

v^2= (at)^2 {squaring both sides}

Therefore,

W= 1/2 mv^2 ____ [using equations (3) and (4)]

The kinetic energy gained by an object is the amount of work done on the object.

Therefore,

K.E.= W

K.E.= 1/2 mv^2

I hope this answer helps!

Good luck!