Question

Derrive the formula for the kinetic energy of and object of Mass m, moving with velocity v. ​

Answer 1

Answer:

Let the workdone on the object causes a change in its velocity from u to V and let a be the acceleration. we know that the kinetic energy of a body moving with certain velocity is equal to workdone on the object to acquire that velocity from rest.

Answer 2

Explanation:

Consider a body of mass "m" moving with an initial velocity "u".

A constant force "F" acts on it and the velocity changes to "v".

Let "s" be the distance covered and "a" be the constant acceleration

We know that

v² - u² = 2as

s = \frac{v^{2} - u ^{2} }{2a}

2a

v

2

−u

2

We know that ,

Work done = Force(F) × displacement (s)

F = ma

W = ma ×\frac{v^{2} - u ^{2} }{2a}

2a

v

2

−u

2

["a" gets cancelled ]

W = m ×\frac{v^{2} - u ^{2} }{2}

2

v

2

−u

2

= \frac{1 }{2}

2

1

m[v² - u² ]

When , initial velocity , u = 0

W = \frac{1 }{2}

2

1

mv²

K.E = Work done

= \frac{1 }{2}

2

1

mv²

i hope it will helps you