Mathematics

Problem

During the algebraic derivation of the work–energy theorem, the element of work is written as

dW = m a\,dx

and then converted to

dW = m v\,dv

. Which mathematical substitution justifies this conversion? a) Using

a = v\,\dfrac{dx}{dv}

b) Using

a = v\dfrac{dv}{dx}

only c) Using

a = \dfrac{dv}{dx}

only d) Using

a = \dfrac{dv}{dt}

and

dt = v\,dx