- #1

A typical automobile has a maximum deceleration of about 7m/s^2; the typical reaction time to engage the brakes is 0.50 s. A school board sets the speed limit in a school zone to meet the condition that all cars should be able to stop in a distance of 4 m.

a) what maximum speed should be allowed for a typical automobile? (Answer = 10.6 m/hr)

b) what fraction of the 4 m is due to the reaction time (Answer = 2.38 m)

* Now i know that part b will be a piece of cake if i get part a. But whenever i do part a (its been several tries...) i get around 13.6 miles per hour, not 10.6.

* Also, it really irks me that i can't figure out these kinematics problems without any help. The book they come from is " Paul A. Tipler physics for scientists and engineers." This book shows the answers, but it doesn't show how they got the answers, so i can't learn how to do them.

* In conclusion, if anyone could point me in the right direction, i'd appreciate it. Also, does anyone know how to learn this stuff so i can do it on my own. I can draw out the situation, so i think i understand it conceptually. Is algebra skills holding me back (like setting the problem up, maybe that's where I am messing up). so should i just try more problems, may b easier so i can work my way up and do problems like these? or go back to the basic concepts?

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What I've got so far is as follows:

The first .5 s of the 4 m there is no acceleration (reaction time). So the distance of the first part of the 4 m traveled (lets say "x") is Vo/2. (From X = Xo + Vavg*t). The second part is where the acceleration is, and you are going to end up at rest. So the distance of the 2nd part of the 4m (let's say "4-x") is (Vo/2)*(t-.5s). If i re arrange this equation i get x = 4 - ((2Vo*t - Vo)/4). So i can set this x equal to Vo/2. I can simplify to get Vo = 16/(2t+3) , or t = (16 - 3*Vo)/(2Vo). If i go back to where t = .5 s and plug that in, i get Vo = 4 m/s. If i change 4m/s to mi/h, i get 8.948 mi/hr. NOT the right answer. (and I am not sure what i did different, but last time i got 13.67 mi/hr)

- What am i doing wrong?