Two cars start off to race velocity $4\text{m/s}\text{and}2\text{m/s}$ & travel in straight line with uniform acceleration $1{\text{m/s}}^2\text{and}2{\text{m/s}}^2$ respectively. if with they reach the final point at the same instant, then the length of the path is:

car A                                                                car B

${\text{u}}_{\text{1}}=4\text{m/s}$                                          ${\text{u}}_2=2\text{m/s}$

${\text{a}}_1=1{\text{m/s}}^{\text{2}}$                                          ${\text{a}}_{\text{2}}=2{\text{m/s}}^{\text{2}}$

${\text{t}}_{\text{1}}={\text{t}}_{\text{2}}$

${\text{s}}_{\text{1}}=4{\text{t}}_1+\frac{1}{2}\left(1\right){\text{t}}_{\text{1}}^{\text{2}}$                             ${\text{s}}_{\text{2}}{\text{=2t}}_2+\frac{1}{2}\times 2\times {\text{t}}_{\text{2}}^{\text{2}}$

$=4{\text{t}}_{\text{1}}+\frac{{\text{t}}_{\text{1}}^{\text{2}}}{\text{2}}$                                           ${\text{s}}_{\text{2}}=2{\text{t}}_{\text{2}}+{\text{t}}_{\text{2}}^{\text{2}}$

${\text{s}}_{\text{1}}={\text{s}}_{\text{2}};{\text{t}}_{\text{1}}={\text{t}}_{\text{2}}$

$\text{4t}+\frac{{\text{t}}^{\text{2}}}{\text{2}}\Rightarrow 2\text{t}+{\text{t}}^{\text{2}}$

$2\text{t}=\frac{{\text{t}}^{\text{2}}}{\text{2}}\Rightarrow \text{t}=4\text{s}$

${\text{s}}_1=4\left(4\right)+\frac{1}{2}\left(1\right){\left(4\right)}^2$

$=16+8=24\text{m}$