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
Vo = 95000m/h * (1h/3600s) = 26.4m/s.
d1 = 26.4m/s * 1s = 26.4m due to human reaction time.
Vf^2 = Vo^2 + 2ad,
d = (Vf^2-Vo^2) / 2a + d1,
d = ((0-(26.4)^2) / -10.4) + 26.4,
d = 67 + 26.4 = 93.4m = total stopping distance.
b Same procedure as a.
Why did the chicken cross the road? To calculate its stopping distance, of course! Let's get to it.
(a) For an acceleration of -5.2 m/s^2, the automobile's stopping distance can be determined using the following formula:
Stopping distance = (initial velocity * reaction time) + (0.5 * acceleration * (reaction time)^2)
Since the initial speed is given as 95 km/h, we first need to convert it to m/s:
95 km/h = (95 * 1000) / (60 * 60) = 26.39 m/s
Plugging the values into the formula, we have:
Stopping distance = (26.39 * 1.0) + (0.5 * -5.2 * (1.0)^2)
= 26.39 - 2.6
= 23.79 m
Therefore, the stopping distance for an acceleration of -5.2 m/s^2 is approximately 23.79 meters.
(b) Now, let's calculate the stopping distance for an acceleration of -6.7 m/s^2. Using the same formula, we have:
Stopping distance = (26.39 * 1.0) + (0.5 * -6.7 * (1.0)^2)
= 26.39 - 3.35
= 23.04 m
So, the stopping distance for an acceleration of -6.7 m/s^2 is approximately 23.04 meters.
Remember, these calculations assume constant acceleration and neglect other factors like friction, weather, and road conditions. Drive safely and don't forget to keep your clown nose on for added protection!
To determine the stopping distances for an automobile, we need to consider two components: the distance covered during the human reaction time and the distance covered due to deceleration.
The formula to calculate the distance covered during the human reaction time is given by:
Distance_reaction = Initial_speed * Reaction_time
Let's calculate the distance covered during the human reaction time for an initial speed of 95 km/h (26.4 m/s) and a reaction time of 1.0 s:
Distance_reaction = 26.4 m/s * 1.0 s = 26.4 m
Now, to calculate the distance covered due to deceleration, we need to use the following formula:
Distance_deceleration = (Final_speed^2 - Initial_speed^2) / (2 * Acceleration)
We are given the initial speed and acceleration. We need to find the final speed when the car comes to a complete stop (v = 0).
(a) For an acceleration of a = -5.2 m/s^2:
Using the equation of motion:
Final_speed^2 = Initial_speed^2 + 2 * Acceleration * Distance_deceleration
0 = (26.4 m/s)^2 + 2 * (-5.2 m/s^2) * Distance_deceleration
Simplifying the equation:
Distance_deceleration = (26.4 m/s)^2 / (2 * 5.2 m/s^2)
Distance_deceleration = 342.86 m
Therefore, the stopping distance for an automobile with an initial speed of 95 km/h and acceleration of -5.2 m/s^2 is 342.86 meters.
(b) For an acceleration of a = -6.7 m/s^2:
Using the same equation of motion:
0 = (26.4 m/s)^2 + 2 * (-6.7 m/s^2) * Distance_deceleration
Simplifying the equation:
Distance_deceleration = (26.4 m/s)^2 / (2 * 6.7 m/s^2)
Distance_deceleration = 231.46 m
Therefore, the stopping distance for an automobile with an initial speed of 95 km/h and acceleration of -6.7 m/s^2 is 231.46 meters.