Determine the stopping distances for an automobile going a constant initial speed of 97km/h and human reaction time of 0.50s , for an acceleration a=−6.5m/s2
***Convert initial speed to m/s
a=-6.5m/s^2
Vf=0
d=?
***Vi=97km/h*(10^3m/1km)*(1h/3600s)=27m/s
Use the following equation and solve for d:
Vf^2=Vi^2+2ad
0^2=(27m/s)^2+2(-6.5m/s^2)d
729=13d
Solving for d,
729/13=d
d=56m
correct.
wrong
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To determine the stopping distance, we need to consider two components: the distance traveled during the driver's reaction time and the distance traveled while decelerating.
1. Distance during reaction time:
During the reaction time, the car is still traveling at its initial speed. The distance covered can be calculated using the formula:
distance = speed * time
Given:
Initial speed (v0) = 97 km/h = 97,000 m/3600 s ≈ 26.94 m/s
Reaction time (t) = 0.50 s
Therefore, the distance covered during the reaction time is:
distance_reaction = v0 * t
distance_reaction = 26.94 m/s * 0.50 s
distance_reaction = 13.47 m
2. Distance traveled while decelerating:
The car is subject to an acceleration (a = -6.5 m/s^2) to eventually come to a stop. To find the distance traveled while decelerating, we can use the following formula:
distance = (final_velocity^2 - initial_velocity^2) / (2 * acceleration)
First, we need to find the final velocity (vf) when the car comes to a stop:
vf = 0 m/s (as it is stopping completely)
Using the given initial velocity (vi) of 26.94 m/s and the final velocity (vf) of 0 m/s, we can calculate the distance traveled while decelerating:
distance_deceleration = (vf^2 - vi^2) / (2 * a)
distance_deceleration = (0^2 - 26.94^2) / (2 * (-6.5))
distance_deceleration = (-726.7236) / (-13)
distance_deceleration ≈ 55.9 m
3. Total stopping distance:
The total stopping distance is the sum of the distance during the reaction time and the distance traveled while decelerating:
total_stopping_distance = distance_reaction + distance_deceleration
total_stopping_distance ≈ 13.47 m + 55.9 m
total_stopping_distance ≈ 69.4 m
Therefore, the stopping distance for the automobile traveling at a constant initial speed of 97 km/h, with a human reaction time of 0.50 s, and acceleration of -6.5 m/s^2 is approximately 69.4 meters.