Col. John Stapp led the U.S. Air Force Aero Medical Laboratory's research into the effects of higher accelerations. On Stapp's final sled run, the sled reached a speed of 284.4 m/s (632 mi/h) and then stopped with the aid of water brakes in 1.4 s. Stapp was barely conscious and lost his vision for several days but recovered.
a.)Determine his acceleration while stopping.
b.)Determine the distance he traveled while stopping.
a = (-284.4 m/s)/1.4s = -203.1 m/s^2
s = Vo t + 1/2 at^2
= 284.4*1.4 - 1/2 (203.1)(1.4^2)
= 199.1 m
a.) Col. John Stapp's acceleration while stopping can be determined using the formula for acceleration:
Acceleration (a) = Change in velocity (Δv) / Time (t)
Given that the sled went from a speed of 284.4 m/s to 0 m/s in 1.4 seconds, we can calculate the change in velocity:
Δv = 0 m/s - 284.4 m/s = -284.4 m/s
Now we can substitute the values into the formula to find the acceleration:
Acceleration (a) = (-284.4 m/s) / 1.4 s
Using a calculator, we find that the acceleration is approximately -203 m/s².
b.) To determine the distance traveled while stopping, we can use the equation:
Distance (d) = Initial velocity (v) * Time (t) + (1/2) * Acceleration (a) * Time (t)²
Since the initial velocity is 284.4 m/s, time is 1.4 seconds, and acceleration is -203 m/s², we can calculate the distance:
Distance (d) = (284.4 m/s) * (1.4 s) + (1/2) * (-203 m/s²) * (1.4 s)²
Using a calculator, we find that the distance traveled while stopping is approximately 415.61 meters.
To determine the acceleration while stopping, we can use the following equation:
acceleration = (final velocity - initial velocity) / time
Plugging in the given values:
Initial velocity (vi) = 284.4 m/s
Final velocity (vf) = 0 m/s (since the sled stopped)
Time (t) = 1.4 s
acceleration = (0 - 284.4) m/s / 1.4 s
acceleration = -204 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
To determine the distance traveled while stopping, we can use the following equation:
distance = (initial velocity + final velocity) / 2 * time
Plugging in the given values:
Initial velocity (vi) = 284.4 m/s
Final velocity (vf) = 0 m/s
Time (t) = 1.4 s
distance = (284.4 + 0) / 2 * 1.4 s
distance = 199.68 m
Therefore, Stapp traveled a distance of approximately 199.7 meters while stopping.
To solve this problem, we'll need to use the kinematic equation that relates acceleration, initial velocity, final velocity, and time.
a) To determine the acceleration, we'll use the equation:
acceleration (a) = (final velocity - initial velocity) / time
Given:
Initial velocity (vi) = 284.4 m/s (since he reached the maximum speed before stopping)
Final velocity (vf) = 0 m/s (since he stopped)
Time (t) = 1.4 s
Using the given values in the equation, we can calculate the acceleration:
a = (0 - 284.4) m/s / 1.4 s
a = -204 m/s²
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which makes sense since the sled is decelerating (coming to a stop).
b) To determine the distance traveled while stopping, we can use another kinematic equation:
distance (d) = (initial velocity + final velocity) / 2 * time
Given:
Initial velocity (vi) = 284.4 m/s
Final velocity (vf) = 0 m/s
Time (t) = 1.4 s
Using the given values in the equation, we can calculate the distance:
d = (284.4 + 0) m/s / 2 * 1.4 s
d = 142.2 m
Therefore, the distance traveled while stopping is 142.2 meters.