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Two cars A and B are moving in the same direction with velocities $v_A = 30 \text{ km/h}$ and $v_B = 20 \text{ km/h}$. When car A is $10 \text{ km}$ behind car B, car A accelerates at $a_A = 4 \text{ km/h}^2$ and car B decelerates at $a_B = -6 \text{ km/h}^2$. How long will it take for car A to overtake car B?
- A.0.5 hours
- B.1 hour
- C.2 hours
- D.1.5 hours
Show correct answer & step-by-step solution
Correct answer: B — 1 hour
Solution
Relative velocity . Relative acceleration . Using , we get , which simplifies to . Solving for gives hour.
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