problem. How long does it take an automobile traveling in the left laneof a high
ID: 1736914 • Letter: P
Question
problem. How long does it take an automobile traveling in the left laneof a highway at 60.0 km/h to overtake (become even with) anothercar that is traveling in the right lane at 40.0 km/h when the car'sfront bumpers are initially 100m apart?Please help. Thank you in advance. How long does it take an automobile traveling in the left laneof a highway at 60.0 km/h to overtake (become even with) anothercar that is traveling in the right lane at 40.0 km/h when the car'sfront bumpers are initially 100m apart?
Please help. Thank you in advance.
Explanation / Answer
You're given two cars at different speeds and you want to know whenone car will catch up with the next one. First you find the equation for the cars since the cars have constant velocity and no acceleration(whichyou'll learn about later), they follow the position equation y=mx+bwhere m is the velocity, x is the time and b is the position Left Car: velocity = 60 km/h its position isn't mentioned except for the fact that the frontbumper of this car is 100m apart from the other car so we'll saythat this car starts from position 0m while the other car startsfrom position 100m. So the equation for this car's position is t(60km/h)= 0 Right Car: velocity = 40 km/h position = 100m (to keep units similar, we convert m to km so 100mbecomes .1km) and this car's position is t(40km/h)+ 0.1=0 where t is the time. now that we have the two equations, we're trying to find the pointwhich the left car is at the same position as the right car so wesolve for t by subtracting the two equations. 40t+100-(60t)=-20t+0.1 and now we solve for t 20t=0.1 t=0.005 hours (if you want to keep your final answer in SI units,convert hours to seconds which will give you 18 seconds) To check if its right, substitute the value back into the equationto see if the position is the same: 40(.005)+100=0.3km 60(.005)=.3km By substituting the value back into the equation, you also find thedistance which they catch up to each other which is .3km or300m.
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