Question

check the correctness of the following equation
$k = 1 \div 2v {}^{2} + ma$

Answer 1

The correct equation is
$E_k = \frac{1}{2} mv^{2}$
According to the work energy theoram,
$W_{12} = \int _1^2 F . dr$
$F . dr = m \times \frac{dv}{dt} \times vdt$
$W_{12} = \frac{1}{2} mv^{2}_{2} - \frac{1}{2} mv^{2}_{1}$
So work done is equal to,
$\Delta E_k$