Determine the stopping distances for an automobile with an initial speed of 95km/h and human reaction time of 1.0s:
(a) for an acceleration a= -5.2m/s^2
(b) for a= -6.7m/s^2
change speed to m/s
Vf^2=Vi^2+2ad solve for d.
oh yes, add distance Vi*.1 to each of those distances.....
To determine the stopping distances, we need to consider two components: the distance covered during the human reaction time and the distance covered during the deceleration.
Step 1: Convert the initial speed from km/h to m/s.
Given initial speed = 95 km/h
1 km/h = 0.277778 m/s
Therefore, initial speed = 95 km/h * 0.277778 m/s = 26.3889 m/s
Step 2: Calculate the distance covered during the human reaction time.
Given reaction time = 1.0 s
The distance covered during the reaction time can be calculated using the formula: distance = speed * time.
Therefore, distance = 26.3889 m/s * 1.0 s = 26.3889 m
Step 3: Calculate the distance covered during deceleration for each case.
(a) For acceleration a = -5.2 m/s^2:
The deceleration in this case is negative, indicating that the car slows down.
To calculate the stopping distance during deceleration, we need to use the following kinematic equation: distance = (initial speed)^2 / (2 * acceleration).
Using this equation, the stopping distance can be calculated as:
distance = (26.3889 m/s)^2 / (2 * (-5.2 m/s^2)) = 71.5804 m
Therefore, the stopping distance for an acceleration of -5.2 m/s^2 is 71.5804 m.
(b) For acceleration a = -6.7 m/s^2:
Using the same kinematic equation as above, the stopping distance can be calculated as:
distance = (26.3889 m/s)^2 / (2 * (-6.7 m/s^2)) = 51.2615 m
Therefore, the stopping distance for an acceleration of -6.7 m/s^2 is 51.2615 m.
In summary:
(a) For an acceleration of -5.2 m/s^2, the stopping distance is 71.5804 m.
(b) For an acceleration of -6.7 m/s^2, the stopping distance is 51.2615 m.
To determine the stopping distances for an automobile with an initial speed of 95 km/h and a human reaction time of 1.0s, we can use the equations of motion.
First, we need to convert the initial speed from km/h to m/s. Since 1 km = 1000 m and 1 hour = 3600 seconds, we have:
Initial speed = 95 km/h = (95 * 1000) / 3600 = 26.39 m/s
Now let's calculate the stopping distances for the given accelerations:
(a) For an acceleration (a) of -5.2 m/s^2:
To find the stopping distance, we need to consider two parts: the distance covered during the reaction time and the distance covered during the deceleration.
1. Distance during the reaction time:
During the reaction time of 1.0s, the car will continue to move at a constant speed. The distance covered during this time can be calculated using the formula:
Distance (d1) = Initial speed * Reaction time
d1 = 26.39 m/s * 1.0s = 26.39 m
2. Distance during deceleration:
To calculate the distance covered during deceleration, we can use the equation of motion:
Distance (d2) = (Initial speed^2 - Final speed^2) / (2 * Acceleration)
Here, the final speed is 0 m/s since the car comes to a stop.
d2 = (26.39^2 - 0^2) / (2 * (-5.2)) = -693.26 m
We have a negative value here because the car is decelerating.
Now, the total stopping distance is the sum of the distance covered during the reaction time and the distance covered during deceleration:
Total Stopping Distance = d1 + d2
Total Stopping Distance = 26.39 m + (-693.26 m) = -666.87 m
Therefore, for an acceleration of -5.2 m/s^2, the stopping distance is approximately -666.87 m, where the negative sign indicates that it is in the opposite direction of the initial motion.
(b) For an acceleration (a) of -6.7 m/s^2:
Using the same process as above, we can calculate the stopping distance.
1. Distance during the reaction time:
d1 = 26.39 m/s * 1.0s = 26.39 m
2. Distance during deceleration:
d2 = (26.39^2 - 0^2) / (2 * (-6.7)) = -206.96 m
Total Stopping Distance = d1 + d2
Total Stopping Distance = 26.39 m + (-206.96 m) = -180.57 m
Therefore, for an acceleration of -6.7 m/s^2, the stopping distance is approximately -180.57 m. Again, the negative sign indicates that it is in the opposite direction of the initial motion.