Question

Two cars $$C_1$$ and $$C_2$$ moving in the a same direction on a straight single lane road with velocities $$12 m/s$$ and $$10 m/s$$ respectively. When the separation between the two was $$200 m,$$ $$C_2$$ started accelerating to avoid a collision. What is the minimum acceleration of car $$C_2$$ so that they don't collide?

A
1cm/s2
B
4cm/s2
C
2cm/s2
D
3cm/s2

Solution

The correct option is A $$1 cm/s^2$$The collision is just avoided if relative velocity becomes zero just at the moment the two cars meet each other.$$v_{12} = 0\, when\, s_{12} = 200$$$$u_{12} = 2, \bar{a}_{12} = -a$$ and $$s_{12} = 200$$$$v^{2}_{12} - u^{2}_{12} = 2a_{12}s_{12}$$$$0 - 2^{2} = -2 \times a \times 200$$$$a = \displaystyle \frac{1}{100}\, m/s^{2} = 0.01\, m/s^{2} = 1\, cm/s^{2}$$Physics

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