Question

Two cars are travelling towards each other on a straight road with velocities 10 m$s^{-1}$ and 12 m$s^{-1}$ respectively. When they are 150 m apart, both drivers apply their brakes and each car decelerates at 2 m$s^{-2}$ until it stops. How far apart will they be when they have come to rest?

• A. 89 m
• B. 98 m
• C. 108 m
• D. 150 m

Answer 1

Answer: (A)

89 m

Distance between the two cars is 150 m.

For $Car-1:$

$v=u_1-at$

$0=10–2t$

t = 5 sec

so distance travelled will be

$s_1=u_{1}t-\frac{1}{2}a{t}^2$

$s_1=10\times 5-\frac{1}{2}\times 2\times 5^2$

$s_1=25m$

For $Car-2:$

$v=u_2-at$

$0=12–2t$

$t=6sec$

so distance travelled will be

$s_2=u_{2}t-\frac{1}{2}a{t}^2$

$s_2=12\times 6-\frac{1}{2}\times 2\times 6^2$

$s_2=36m$

So, when both cars will stop then the distance between them, will be :

$150m–(25+36)m$

$=89m$

Option A is correct.