An airplane that is flying level needs to accelerate from a speed of 200 𝑚/𝑠 to a speed of 240 𝑚/𝑠while it flies a distance of 1200 𝑚. What must the acceleration of the plane be?
Question
An airplane that is flying level needs to accelerate from a speed of 200 𝑚/𝑠 to a speed of 240 𝑚/𝑠while it flies a distance of 1200 𝑚. What must the acceleration of the plane be?
Solution
To solve this problem, we can use the equation of motion:
v^2 = u^2 + 2as
where: v = final velocity = 240 m/s u = initial velocity = 200 m/s a = acceleration (which we are trying to find) s = distance = 1200 m
Rearranging the equation to solve for acceleration gives us:
a = (v^2 - u^2) / (2s)
Substituting the given values into the equation gives us:
a = ((240 m/s)^2 - (200 m/s)^2) / (2 * 1200 m) a = (57600 m^2/s^2 - 40000 m^2/s^2) / 2400 m a = 17600 m^2/s^2 / 2400 m a = 7.33 m/s^2
So, the acceleration of the plane must be 7.33 m/s^2.
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