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A car is traveling at a constant speed of 33 $\mathrm{m} / \mathrm{s}$ 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 twocars meet for the first time at the next exit, which is 2.5 $\mathrm{km}$ away?

$a=.87 \frac{m}{s^{2}}$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

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Lectures

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Okay, We have one car moving at a constant speed of 33 meters per second. Another car starts from rest. So be not, is zero and accelerates at some acceleration. And they the two cars meet at a later point at 2.5 kilometers or 2500 meters from their initial position. So we need to calculate that acceleration. Um, it might be helpful to visualize this in a graph. One car is moving at a constant speed up. This is a position versus time graph one car, the first car car, one moving at a constant speed. The other car starts from rest and speeds up. So here's where they meet at the 2500 meter position after having been at the same place at the same time at the beginning of the problem. So we don't have time, but it is easy to find the time. If you look at Car one car one. The distance distance for car one is just velocity times T because there's no acceleration. So 2500 meters is equal to 33 meters per second, claims the time rearranging that we have a time interval of 75.76 seconds. So now we have a tea. So our next job is to calculate what the acceleration must be for car to in order to reach a 25 meet 100 meter distance. So let's use this equation. Me not tea plus 1/2 a T squared. So plugging my numbers in for car to 2500 meters, the initial is zero, so I don't even have to put that into the equation. 1/2 a time. 75.76 seconds squared so I can do the ultra 75.76 square divided by two. And then I guess I could multiply both sides by two and then divide both sides by 75.76 seconds squared and we have an acceleration of 0.8712 meters per second squared rounded to two significant figures 0.87 meters per second squared

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