A particle whose speed is 50 m/s moves along the line from A(2, 1) to B(9, 25). Find the velocity vector in the form of $\mathrm{a}\widehat{\mathrm{i}}+\mathrm{b}\widehat{\mathrm{j}}$

$\overrightarrow{\mathrm{V}}=50\left(\widehat{AB}\right)$

$\left|\overline{\mathrm{AB}}\right|=(9-2)\widehat{\mathrm{i}}+(25-1)\widehat{\mathrm{j}}=(7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}})$

$\left|\overline{\mathrm{AB}}\right|=\sqrt{{\left(7\right)}^2+{\left(24\right)}^2}$

$\widehat{AB}=\frac{(7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}})}{\sqrt{{\left(7\right)}^2+{\left(24\right)}^2}}=\frac{(7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}})}{25}$

$\overrightarrow{\mathrm{V}}=50.\frac{(7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}})}{25}=2(7\widehat{\mathrm{i}}+24\widehat{\mathrm{j}})\mathrm{m}/\mathrm{s}$