2) An aircraft lands on a runway at a speed of 40 meters per second (ms^-1) and brakes to a halt in a distance of 860m. Calculate a) The Braking time. B) The deceleration of the aircraft.
a=v²/2s = 40²/2•860=0.93 m/s²
v= v₀-at
v=0
t= v₀/a =40/0.93 =43.01 s.
a=v²/2s
v= v₀-at
v=0
t= v₀/a
Not really helping much. A slightly worked example would be effective. But thanks anyway.
Yes, thank you. I worked it out, after a few minutes. Anyway, thank's a lot :)
a) The braking time can be calculated using the formula:
Braking time = Distance / Speed
Given that the distance is 860 meters and the speed is 40 meters per second, we can plug in the values:
Braking time = 860m / 40ms^-1
Calculating the result:
Braking time = 21.5 seconds
b) The deceleration of the aircraft can be calculated using the formula:
Deceleration = (Final Speed - Initial Speed) / Time
Since the aircraft comes to a halt, the final speed is 0, the initial speed is 40 m/s, and the time is 21.5 seconds (from part a), we can substitute these values into the formula:
Deceleration = (0 - 40) / 21.5
Calculating the result:
Deceleration = -1.86 ms^-2
So, the deceleration of the aircraft is approximately -1.86 meters per second squared. Wow, that's negative! It must have really wanted to stop!
To calculate the braking time and deceleration of the aircraft, we can use the basic kinematic equation for motion:
v² = u² + 2as
Where:
v = final velocity (0 m/s, as the aircraft comes to a halt)
u = initial velocity (40 m/s)
a = acceleration (which is the deceleration in this case)
s = distance (860 m)
a) The Braking time:
Since we want to find the braking time, we need to rearrange the equation:
v² = u² + 2as
Rearranging for time (t):
t = (v - u) / a
In this case, v = 0 m/s and u = 40 m/s. We can substitute these values into the equation:
t = (0 - 40) / a
Next, we need to find the value of acceleration (a) in order to calculate the braking time. We can rearrange the above equation to solve for a:
a = (0 - 40) / t
Now, we can substitute the given distance (s = 860 m) to solve for time (t):
860 = (40*t) + (0.5 * a * t²)
Simplifying this equation, we can see that the acceleration term (0.5 * a * t²) is negligible compared to 40*t.
Therefore, we can approximate the equation to:
860 ≈ 40t
Dividing both sides by 40, we get:
t ≈ 21.5 seconds
So, the braking time is approximately 21.5 seconds.
b) The deceleration of the aircraft:
Now that we know the braking time, we can substitute this value of t back into the equation:
a = (0 - 40) / t
a = (0 - 40) / 21.5
Simplifying, we find:
a ≈ -1.86 m/s²
The negative sign indicates that the aircraft is decelerating.
Therefore, the deceleration of the aircraft is approximately -1.86 m/s².