A car A is travelling on a straight level road with a uniform speed of 60 km ph. It is followed by another car B which is moving with a speed of 70 km ph. When the distance between them is 2.5 km, the car B is given a deceleration of $20{\text{kmh}}^{-2}.$  The distance and time after which the car B catches up with the car, A are

${\text{Let t}}_1=\text{t}$                                  ${\text{x}}_{\text{AB}}={\text{S}}_{\text{AB}}=\text{2}\text{.5km}$      $\text{ab}=-2{\text{0kmph}}^{-2}$

${\text{The time interval t the distance travelled by X}}_{\text{A}}{\text{andX}}_{\text{B}}$

${\text{x}}_{\text{A}}=\text{60t}$                                  ${\text{ x}}_{\text{B}}=70\text{t}-\frac{1}{2}\left(20\right){\text{t}}^{\text{2}}$

$\text{aA}=\text{0}$

$X_{AB}={\text{X}}_{\text{A}}-{\text{X}}_{\text{B}}=2.5$

$\text{60t}-7\text{0t}+{\text{10t}}^2=2.5$

$\text{t}=0.\text{5 hour}$

${\text{x}}_{\text{A}}=60\left(\frac{1}{2}\right)=30\text{km}$

$\text{The total distance }=\text{30}+\text{2}\text{.5}$ $=\text{32}\text{.5kms}$