Question

Two cars are travelling towards each other on straight road at velocities 15m/s and 16m/s respectively .when they are 150m apart, both the drivers apply the breaks and the cars decelerates at 3m/s² and 4m/see until they stop. How for apart will they be when they come to a stop ?

Answer 1

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Answer 2

Answer:

The distance between the cars after coming to stop is 80.5 m

Explanation:

Given that,

Total distance = 150 m

The velocity of both cars

$v_{1}= 15\ m/s$

$v_{2}=16\ m/s$

The acceleration of both cars using the breaks

$a_{1}= -3\ m/s$

$a_{2}=-4\ m/s$

Case (I)

The distance of first car is

Using equation of motion

$v_{1}^2-u^2=2a_{1}s_{1}$.....(I)

Where,

v = final velocity

u = initial velocity

a = acceleration

s = distance

Put the value into the equation (I)

$0-15^2=2\times(-3)\times s_{1}$

$s_{1}=\dfrac{15\times15}{6}$

$s_{1}= 37.5\ m$

Case (II)

The distance of second car is

Using equation of motion

$v_{2}^2-u^2=2a_{2}s_{2}$.....(I)

Where,

v = final velocity

u = initial velocity

a = acceleration

s = distance

Put the value into the equation (I)

$0-16^2=2\times(-4)\times s_{2}$

$s_{2}=\dfrac{16\times16}{8}$

$s_{2}= 32\ m$

The distance between the cars after coming to rest is

$s' = 150-(37.5+32)$

$s'=80.5\ m$

Hence, The distance between the cars after coming to stop is 80.5 m.