A car A is travelling on a straight level road with a uniform spe… - Vidyadip

MCQ

A car $A$ is travelling on a straight level road with a uniform speed of $60$$km/h.$It is followed by another car $B$ which is moving with a speed of $70$ $km/h.$When the distance between them is $2.5\, km$, the car $B$ is given a deceleration of $20$$km/{h^2}.$ After how much time will $ B$ catch up with $A$...........$hr$

A
$1$
✓
$0.5$
C
$0.25$
D
$1/8$

✓

Answer

Correct option: B.

$0.5$

b
(b) Let car $B$ catches, car $A$ after $‘t’$ sec, then

$60t + 2.5 = 70t - \frac{1}{2} \times 20 \times {t^2}$

==> $10{t^2} - 10t + 2.5 = 0$==> ${t^2} - t + 0.25 = 0$

$\therefore $ $t = \frac{{1 \pm \sqrt {1 - 4 \times (0.25)} }}{2} = \frac{1}{2}hr$

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