`➢` As we know, the relation for rectilinear motion under constant acceleration
`v^2 − u^2 = 2 as`
`=>` where `u` and `v` are the initial and final speeds and `s` the distance traversed. Multiplying both sides by `m//2`, we have
`color {blue}{1/2 mv^2 - 1/2 m u^2 = mas= Fs}` ..............(6.2a)
`=>` where the last step follows from Newton’s Second Law. We can generalise Eq. (6.1) to three dimensions by employing vectors
`v^2 − u^2 = 2 a*d`
`➢` Once again multiplying both sides by `m//2` , we obtain
`color {blue}{1/2 mv^2 - 1/2 mu^2 = m a * d = F* d}` ..................(6.2b)
`➢` The left side of the equation is the difference in the quantity ‘half the mass times the square of the speed’ from its initial value to its final value.
`➢` We call each of these quantities the ‘kinetic energy’, denoted by `K`. The right side is a product of the displacement and the component of the force along the displacement. This quantity is called ‘work’ and is denoted by `W`. Eq. (6.2) is then
`color {blue}{K_f - K_t = W}`.............(6.3)
`=>` where `K_i` and `K_f` are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement.
Equation (6.2) is also known as `"work-energy (WE) theorem :"` The change in kinetic energy of a particle is equal to the work done on it by the net force. We shall generalise the above derivation to a varying force in a later section.
`➢` As we know, the relation for rectilinear motion under constant acceleration
`v^2 − u^2 = 2 as`
`=>` where `u` and `v` are the initial and final speeds and `s` the distance traversed. Multiplying both sides by `m//2`, we have
`color {blue}{1/2 mv^2 - 1/2 m u^2 = mas= Fs}` ..............(6.2a)
`=>` where the last step follows from Newton’s Second Law. We can generalise Eq. (6.1) to three dimensions by employing vectors
`v^2 − u^2 = 2 a*d`
`➢` Once again multiplying both sides by `m//2` , we obtain
`color {blue}{1/2 mv^2 - 1/2 mu^2 = m a * d = F* d}` ..................(6.2b)
`➢` The left side of the equation is the difference in the quantity ‘half the mass times the square of the speed’ from its initial value to its final value.
`➢` We call each of these quantities the ‘kinetic energy’, denoted by `K`. The right side is a product of the displacement and the component of the force along the displacement. This quantity is called ‘work’ and is denoted by `W`. Eq. (6.2) is then
`color {blue}{K_f - K_t = W}`.............(6.3)
`=>` where `K_i` and `K_f` are respectively the initial and final kinetic energies of the object. Work refers to the force and the displacement over which it acts. Work is done by a force on the body over a certain displacement.
Equation (6.2) is also known as `"work-energy (WE) theorem :"` The change in kinetic energy of a particle is equal to the work done on it by the net force. We shall generalise the above derivation to a varying force in a later section.