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An engineer must design a runway to accommodate airplanes that must reach a ground velocity of 61 m/s before they can take off. these planes are capable of being accelerated uniformly at a rate of 2.5 m/s²?

a) how long will it take the planes to reach takeoff speed?

User Reko
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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.

User Johnny Utahh
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