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Standard XII

Physics

Acceleration in 2D

Two cars are ...

Question

Two cars are travelling towards each other on a straight road at velocities $15 m / s$ and $16 m / s$ respectively. When they are $150 m$ apart, both the drivers apply the brakes and the cars decelerate at $3 m / s^{2}$ and $4 m / s^{2}$ until they stop. Separation between the cars when they come to rest is :

86.5 m

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89.5 m

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85.5 m

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80.5 m

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Solution

The correct option is D $80.5 m$
We know, $v^{2} = u^{2} - 2 a s$

Given,

Initial velocity of car 1, $u_{1} = 15 m / s$ , Acceleration, $a = 3 m / s^{2}$

Initial velocity of car 2, $u_{2} = 16 m / s$ , Acceleration, $a = 4 m / s^{2}$

For car 1,

Final Velocity, $v_{1} = 0 m / s$

$- 15^{2} = - 2 (3) \times s$

$∴ s_{1} = 37.5$ m

For car 2,

Final Velocity, $v_{2} = 0 m / s$

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

$∴ s_{2} = 32$ m

Total displacement,

$s_{1} + s_{2} = 37.5 + 32 = 69.5$ m

$∴$ separation between them,

$= 150 - 69.5 = 80.5$ m

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Two cars are travelling towards each other on a straight road at velocities 15 m/s and 16 m/s respectively. When they are 150 m apart, both the drivers apply the brakes and the cars decelerate at 3 m/s2 and 4 m/s2 until they stop. Separation between the cars when they come to rest is :