A car is traveling at a constant speed of 23 m/s on a highway. at the instant this car passes an entrance ramp, a second car enters the highway from the ramp. the second car starts from rest and has a constant acceleration. what acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is 3.0 km away?

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01-09-2017
Physics

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A car is traveling at a constant speed of 23 m/s on a highway. at the instant this car passes an entrance ramp, a second car enters the highway from the ramp. the second car starts from rest and has a constant acceleration. what acceleration must it maintain, so that the two cars meet for the first time at the next exit, which is 3.0 km away?

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hankaF hankaF · Answer 1 · 2017-09-14T09:42:44+02:00

23 m/s (dividing by 1000 m/km) = 0.023 km/sDistance (3 km) divided by Speed (0.023 km/s) gives us Time = 130.43478... secSo it takes the first car mentioned about 130 seconds to move from the entrance ramp to the next exit.
We would like the second car to cover the same distance in the same time, but not be traveling at a steady pace, instead start at 0 and constantly increase speed. Even though the speed will be changing each instant, the AVERAGE speed of the second car will be the same as the speed of the first car over those 3 km in order for them to meet again. So the average speed of the second car will be 23 m/s.
Acceleration is a rate of change of speed, (or average speed divided by time). So, to find the acceleration of the second car, we divide 23 m/s by the time 130.43... s. This yields 0.17633333... m/s^2 as the acceleration needed."