An airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of 2.40 x 102 m/s while it flies a distance of 1.20 km.What must the acceleration of the plane be?Express your answer in m/s2.
Question
An airplane that is flying level needs to accelerate from a speed of 2.00 × 102 m/s to a speed of 2.40 x 102 m/s while it flies a distance of 1.20 km.What must the acceleration of the plane be?Express your answer in m/s2.
Solution
To solve this problem, we can use the equation of motion:
v^2 = u^2 + 2as
where: v = final velocity = 2.40 x 10^2 m/s u = initial velocity = 2.00 x 10^2 m/s a = acceleration (which we are trying to find) s = distance = 1.20 km = 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 = ((2.40 x 10^2 m/s)^2 - (2.00 x 10^2 m/s)^2) / (2 * 1200 m)
a = ((57600 m^2/s^2 - 40000 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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