Question

Velocity ($v$) vs. displacement ($s$) graph of a freely falling body is:

• A. Straight line passing through the origin
• B. Straight line interesting $X$ and $Y$ axes
• C. Parabola
• D. Hyperbola

Answer 1

The correct option is C Parabola

Free falling body has constant acceleration, $a=g$.

Therefore: $v\frac{dv}{ds}=g\Rightarrow vdv=gds\Rightarrow {\int }_u^{v}vdv={\int }_0^{s}gds\Rightarrow \frac{v^2-u^2}{2}=gs\Rightarrow v^2=u^2+2gs$

As distance is proportional to square of velocity therefore graph will be a parabola.