Question

Two car travelling towards each other on a straight road at velocity $10\, m / \sec$ and $12\, m / \sec$ respectively. When they are $150\, m$ apart, both drivers apply their brakes and each car decelerates at $2\, m / \sec ^{2}$ until it stops. How far apart will they be when they have both come to a stop?

• A. 8.9 m
• B. 89 m
• C. 809 m
• D. 890 m

Answer 1

Answer: (B)

Let $x_{1}$ and $x_{2}$ be the distance travelled by the car before they stop under deceleration.
Using the formula $v ^{2}= u ^{2}+2 a\, s$,
we have, $0=(10)^{2}-2 \times 2 \times x_{1}$
and $0=(12)^{2}-2 \times 2 \times x_{2}$
Solving we get,
$x_{1}=25$ metre and $x_{2}=36$ metre
Total distance covered by the two cars
$x_{1}+x_{2}=25+36=61$ metre
Distance between the two cars when they stop
$=150-61=89$ metre