Final answer:
It will take approximately 24.4 seconds for the airplanes to reach takeoff speed. To determine how long it will take an airplane to reach takeoff speed with a given acceleration, we can use the following kinematic equation where initial velocity (u) is zero since the plane starts from rest.
Step-by-step explanation:
To find the time it takes for the plane to reach takeoff speed, we can use the formula:
final velocity = initial velocity + (acceleration * time)
Let's assign the values:
final velocity = 61 m/s
initial velocity = 0 m/s (since the plane starts from rest)
acceleration = 2.5 m/s²
We need to find the time (t).
Substituting the given values into the formula:
61 m/s = 0 m/s + (2.5 m/s² * t)
61 m/s = 2.5 m/s² * t
Dividing both sides of the equation by 2.5 m/s²:
t = 24.4 s
Therefore, it will take approximately 24.4 seconds for the planes to reach takeoff speed.
It will take the airplane approximately 24.4 seconds to reach the takeoff speed of 61 m/s starting from rest when it accelerates uniformly at 2.5 m/s².
To determine how long it will take an airplane to reach takeoff speed with a given acceleration, we can use the following kinematic equation where initial velocity (u) is zero since the plane starts from rest:
v = u + at
In this equation, v represents the final velocity, u represents the initial velocity, a represents the acceleration, and t represents the time. Given that the final velocity (v) is 61 m/s and the acceleration (a) is 2.5 m/s², we can rearrange the equation to solve for time (t):
t = (v - u) / a
Substitute the known values:
t = (61 m/s - 0 m/s) / 2.5 m/s² = 24.4 s
Therefore, it will take the airplane approximately 24.4 seconds to reach the takeoff speed of 61 m/s.