Question

Prove that change in the kinetic energy pr unit mass is given by ${\left[\frac{v^2}{2}\right]}_u^v$

Answer 1

Small change in kinetic energy, when velocity change from $utov$

$\int dk=\underset{u}{\overset{v}{\int }}mvdv$

$K.E=m{\left[\frac{v^2}{2}\right]}_u^v$

${\left[\frac{v^2}{2}\right]}_u^v=\frac{K.E}{m}$

Kinetic energy per unit mass is ${\left[\frac{v^2}{2}\right]}_u^v$