# Is the derived formula valid?

• B
ForceBoy
Kinetic Energy is defined as the product of half the mass of an object multiplied by the square of its velocity. Using this I derived the end formula. Work is as follows:

KE = ½(m⋅v2)

Because v = vi +at, if vi = 0,

KE = ½(m⋅(at)2)

KE = ½(m⋅a2⋅t2)

KE = ½(m⋅a⋅a⋅t2)

Substituting F for m⋅a (force is equal to mass by acceleration),

KE = ½(F⋅a⋅t2)

Displacement is equivalent to vi⋅t +½⋅a⋅t2
It was stated that vi = 0, therefore s = ½⋅a⋅t2
Making this replacement in the equation yields:

KE = F⋅ s

Where F is a force and s is a displacement. This is also the formula for work. Then, is work the same thing as Kinetic Energy? Can the formula for work be used to calculate Kinetic Energy?