a) The <em>approximate</em> reaction distance is 66 feet.
b) The <em>approximate</em> braking distance is 802.304 feet.
c) The <em>total</em> distance is 868.304 feet.
<h3>How to analyzing reaction time in a braking event</h3>
The <em>average</em> <em>reaction</em> time (
) is 0.75 seconds. Manuel drives at <em>constant</em> velocity in the first 0.75 seconds, then he <em>decelerates</em> the vehicle.
a) The reaction distance (
), in meters, is found by the following expression:
(1)
Where
is the initial velocity, in feet per hour.
If we know that
(
) and
, then the approximate reaction distance is:
![x_{R} = (88)\cdot (0.75)](https://tex.z-dn.net/?f=x_%7BR%7D%20%3D%20%2888%29%5Ccdot%20%280.75%29)
The <em>approximate</em> reaction distance is 66 feet. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
b) A <em>normal</em> braking has magnitudes of about 0.15 times the value of <em>gravitational</em> acceleration (
). The approximate braking distance (
), in feet, is found by the following <em>kinematic</em> formula:
(2)
Where:
- Deceleration rate, in feet per square second.
- Final velocity, in feet per second.
If we know that
and
, then the approximate braking distance is:
![d = \frac{\left(0\,\frac{ft}{s}\right)^{2}-\left(88\,\frac{ft}{s} \right)^{2}}{2\cdot \left(0.15\right)\cdot \left(-32.174\,\frac{ft}{s^{2}} \right)}](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B%5Cleft%280%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%5Cright%29%5E%7B2%7D-%5Cleft%2888%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%7D%7B2%5Ccdot%20%5Cleft%280.15%5Cright%29%5Ccdot%20%5Cleft%28-32.174%5C%2C%5Cfrac%7Bft%7D%7Bs%5E%7B2%7D%7D%20%5Cright%29%7D)
![d = 802.304\,ft](https://tex.z-dn.net/?f=d%20%3D%20802.304%5C%2Cft)
The <em>approximate</em> braking distance is 802.304 feet. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
c) The <em>total</em> distance is the sum of distances found in a) and b). Then, the <em>total</em> distance is 868.304 feet. ![\blacksquare](https://tex.z-dn.net/?f=%5Cblacksquare)
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