The acceleration vs distance graph for a particle moving with...

Area of graph \begin{array}{l} =\int \mathrm{adx}=\int \frac{\mathrm{vdv}}{\mathrm{dx}} \cdot \mathrm{d} \mathrm{x}==\int_{\mathrm{V}_{\mathrm{i}}}^{\mathrm{v}_{\mathrm{f}}} \mathrm{v} \mathrm{d} \mathrm{v} \\ =\left[\frac{\mathrm{v}^{2}}{2}\right]_{\mathrm{v}_{\mathrm{i}}}^{\mathrm{v}_{\mathrm{f}}}, 150+150=\frac{1}{2}\left[\mathrm{~V}_{\mathrm{f}}^{2}-\mathrm{V}_{\mathrm{i}}^{2}\right] \end{array}\begin{array}{l} 300 \times 2=V_{f}^{2}-(5)^{2} \\ V_{f}^{2}=600+25, V_{f}=25 \end{array}