During takeoff, a plane goes from 0 to 50 m/s in 8s. What is its acceleration? Halos fast is it going after 5 s? How far had it traveled by the time it reaches 50 m/s?
a= 50/8 m/s^2
vf=at=50/8 * 5= 250/8 m/s at t=5sec
time to get to 50m/s
50=50/8*t or t=8 seconds
distance=1/2 a t^2=1/2 50/8 64
distance= 400 m check that.
The answer is actually 200 m because you forgot to divide 400 by 2 from the 1/2.
Bmnkhv
Thank you for setting up the equation, I'm happy I understood it. Although the final answer was off, it wasn't by much, you forgot to divide to get 200. Very grateful for the way you set it up though.
To find the acceleration of the plane during takeoff, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 0 m/s, the final velocity (v) is 50 m/s, and the time (t) is 8 seconds, we can substitute these values into the formula:
acceleration = (50 m/s - 0 m/s) / 8 s
Simplifying the equation gives us:
acceleration = 50 m/s / 8 s
acceleration ≈ 6.25 m/s²
Therefore, the acceleration of the plane during takeoff is approximately 6.25 m/s².
To determine how fast the plane is going after 5 seconds, we can use the formula:
final velocity = initial velocity + (acceleration * time)
Given that the initial velocity (u) is 0 m/s, the acceleration is 6.25 m/s², and the time (t) is 5 seconds, we can substitute these values into the formula:
final velocity = 0 m/s + (6.25 m/s² * 5 s)
Simplifying the equation gives us:
final velocity = 0 m/s + 31.25 m/s
final velocity = 31.25 m/s
Therefore, after 5 seconds, the plane is going approximately 31.25 m/s.
To find the distance the plane has traveled by the time it reaches 50 m/s, we need to use the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
Given that the initial velocity (u) is 0 m/s, the acceleration is 6.25 m/s², and we want to find the time it takes to reach 50 m/s, we'll use the following equation:
50 m/s = 0 m/s + 1/2 * 6.25 m/s² * time^2
Simplifying the equation gives us:
50 = 3.125 * time^2
Dividing both sides of the equation by 3.125 gives:
time^2 ≈ 16
Taking the square root of both sides, we find:
time ≈ 4 s
Now that we know the time it takes to reach 50 m/s is approximately 4 seconds, we can substitute this time into the formula for distance:
distance = initial velocity * time + (1/2) * acceleration * time^2
distance = 0 m/s * 4 s + 1/2 * 6.25 m/s² * (4 s)^2
distance = 0 m + 1/2 * 6.25 m/s² * 16 s²
distance = 1/2 * 6.25 m/s² * 256
distance = 800 m
Therefore, the plane would have traveled approximately 800 meters by the time it reaches 50 m/s.