University of Houston

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Problem 71

Acceleration At the instant the traffic light turns green, a car that has been waiting at an intersection starts with a constant acceleration of 6 feet per second per second. At the same instant, a truck traveling with a constant velocity of 30 feet per second passes the car.

(a) How far beyond its starting point will the car pass the truck?

(b) How fast will the car be traveling when it passes the truck?

Answer

see explanation

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## Discussion

## Video Transcript

question everyone looking at the speed of a truck and a core. So the car they are giving us on, um, acceleration, acceleration of the car and six feet her seconds Where so fine that the, um speed or the velocity we would take the integral of six feet per second's were, which would just give us six t since the these a 00 So our Constance can take care of themselves in this problem and then our x simply are ex empty our position. Gumption, e equals that would be 16 square times, 1/2 game three he squared. And again, I don't worry about mine. Own Constance. Now with the truck, I'm starting out with a B T and that's 30. I'm second position. Function would then be integral of that. Thank you. So now I want to find out When work the distance is equal to each other. I guess that my position functions of each other. Three. He's squared 30 really t squared minus 30 zero. Factor out a three t yet T minus 10 zero t Either equal zero or 10. We're not interested in zero, so e equals 10. That would be in seconds and then part B, we're looking at, um Oh, sorry. Student finished party. I'm so you know that that that 12th. So now I have to put that in our position function. So three times 10 squared. 300. And that will be in no. Three. So then part is asking us to speed. So they put that in my velocity. 56 finds him eat 16 times and we know t to be 10 seconds. That really 10 eaten 16. But that's a week from second. You should really tell us. So we want to change that miles per hour. So do that. 16 feet per second. Times 3600 seconds. Divine by 50 5180 feet in a mile. And when we do that, we get the approximately 41 month

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