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(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by ca

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) Let the time taken for car $B$ to catch up with car $A$ be $t$ hours.Distance covered by car $A$ in time $t$ is $d_A = 60t$.Distance covered by car $B$ in time $t$ with initial velocity $u = 70 	ext{ km/h}$ and deceleration $a = -20 	ext{ km/h}^2$ is $d_B = 70t - \frac{1}{2} 	imes 20 	imes t^2$.Since car $B$ is $2.5 	ext{ km}$ behind car $A$,the condition for catching up is $d_B = d_A + 2.5$.Substituting the expressions: $70t - 10t^2 = 60t + 2.5$.Rearranging the terms: $10t^2 - 10t + 2.5 = 0$.Dividing by $10$: $t^2 - t + 0.25 = 0$.This is a perfect square: $(t - 0.5)^2 = 0$.Therefore,$t = 0.5 	ext{ hours}$.

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