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Carnegie Mellon University



Problem 31 Easy Difficulty

How long does it take an automobile traveling in the left lane of a highway at 60.0 $\mathrm{km} / \mathrm{h}$ to overtake (become even with) another car that is traveling in the right lane at 40.0 $\mathrm{km} / \mathrm{h}$ when the cars' front bumpers are initially 100 $\mathrm{m}$ apart?




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Video Transcript

so we can say that first, the velocity of the fast car relative to the slower car is gonna be equaling the velocity of the fast car relative to the earth, minus the velocity of the slower car relative to the earth. And so we consider the velocity of a fast car relative to the slow car would be 60 kilometers per hour, minus 40 kilometers per hour, giving us 20 kilometers per hour. So that would be the velocity of the fast car relatives to a slow car. We know that the faster car is 100 meters behind the slower car. How long it will it take for them to over for the fast car? To overtake the slow car, you can say T would be equaling 100 meters or 1000.100 kilometers, divided by the velocity of the fast car relatives. The slower car 20 Colombia's per hour multiplied by 3600 seconds for every one hour, and this gives us 18.0 seconds. This is how long it's going to take for the fast car to overtake the slower car. That is the end of the solution. Thank you for watching

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