Calculating Stopping Distance: Reaction Time and Acceleration in Automobiles

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SUMMARY

The discussion focuses on calculating the stopping distance of an automobile based on reaction time and acceleration. The driver's reaction time is established at 0.7 seconds, and the vehicle's deceleration is -4.0 m/s². For an initial speed of 6.7 m/s, the total stopping time is calculated as 2.375 seconds, leading to a stopping distance of 16.1 meters. For an initial speed of 24.6 m/s, the stopping time is 6.15 seconds, resulting in a stopping distance of 66.5 meters.

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courtrigrad
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The reaction time of an automobile driver is about 0.7 s. (reaction time is interval between the perception of a signal to stop and the application of the brakes). If an automobile can slow down with an acceleration of -4.0 m/s^2. compute total distance convered in coming to a stop after a signal is observed (a) from an initial speed of 6.7 m/s in a school zone; (b) from an initial speed of 24.6 m/s.

(a) So I know that [itex]v_{x} = 0, v_{x}_{0} = 6.7 m/s, a_{x} = -4.0 m/s^{2}[/itex]. So would I first find time by using [itex]0 = 6.7 - 4t[/itex] or [itex]t = 1.675 s[/itex]. Then would I add 0.7 seconds to that to get total time? And then use [itex]x = x_{0} + v_{x}_{0}t + \frac{1}{2}a_{x}t^{2}[/itex]. I think something is wrong, but ont know what.

Any help is appreciated

Thanks
 
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This seems like the exact solution method. Why do you think it is wrong?
 

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