Giancoli's Physics: Principles with Applications, 7th Edition

2

Describing Motion: Kinematics in One Dimension

Change chapter2-1 to 2-3: Speed and Velocity

2-4: Acceleration

2-5 and 2-6: Motion at Constant Acceleration

2-7: Freely Falling Objects

2-8: Graphical Analysis

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.

Problem 32

Q

A

$d_T \gt 20.0\textrm{ m}$ so she will not stop in time. She will be $30.7\textrm{ m past the intersection.}$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The total distance this driver will travel will be the distance she travels while reacting to the red light this is before she presses the brakes on and during which there is no deceleration and then add to that the distance that she travels while the brakes are being applied. So the distance traveled during the reaction time is the initial speed times the reaction time so that's 18 meters per second times 0.350 seconds and that gives 6.3 meters and then to figure out the distance traveled while stopping, we use this formula which has all the things known except for the distance while pressing the brakes, while stopping final speed is zero we'll subtract *v i* squared from both sides and we get negative *v i* squared equals *2ad s* for stopping and then divide both sides by *2a* and then switch the sides around and we get *d s* equals negative *v i* squared over *2a*. So that's negative of 18 meters per second squared divided by 2 times the acceleration of negative 3.65 meters per second squared. So that's 44.384 meters traveled while the brakes are being depressed for a total of 50.68 meters distance traveled from the time the red light begins and she has this reaction time distance of 6.3 meters before the brakes are applied plus this. So that's way more than 20 meters away from the intersection and so she'll definitely not stop in time and she'll be 30.7 meters past the intersection by the time she comes to a stop.

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