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Physics Problem

"At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s^2. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile. (a). How far beyond the traffic signal will the automobile overtake the truck? (b). How fast will the automobile be traveling at that instant?"
 

Answers and Replies

Doc Al
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Start by writing the kinematic formulas describing the distance of each as a function of time. One formula will involve accelerated motion; the other, constant speed motion.
 
hmm... I really think I have lost brain cells or something. In the back of the book it has the answers (a). 82m (b). 19 m/s

I get 82m if I use x=(2v^2)/a. But, I'm not sure how to derive that formula.

For the (b), I used v^2 = Vinitial^2 +2a(X-Xinitial) and got 19 m/s
 
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The first equation is derived from the one you used in b.
 
whozum said:
The first equation is derived from the one you used in b.
oh wow, you're right. I never thought that a times x was just v^2. I was not thinking of the dimensions.

So after moving v initial over to the other side, I had delta V^2 = 2 v^2

Then i broke up delta V^2 into v times v. I change one of those into x/1 and 1/t. I combined v and 1/t to get a. So now I had a times x = 2v^2.

I get the first equation of my previous post after dividing by a on both sides.

x = (2v^2)/a


thanks, to both of you
 

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