Answer to Question #125353 in Physics for Josh

Question #125353
A light plane must reach a speed of 33 m/s for takeoff. How long a runway is needed if the acceleration is 3.0 m/s2?
1
Expert's answer
2020-07-06T15:13:12-0400

By definition of the acceleration, to accelerate from the rest to speed v=33m/sv=33m/s with the acceleration a=3m/s2a = 3m/s^2 the plane needs the following amount of time:


t=vat = \dfrac{v}{a}

During this time, plane covers the following distance, according to the kinematic law:


d=at22d = \dfrac{at^2}{2}

Substituting the expression for tt into the last formula, get:


d=v22ad = \dfrac{v^2}{2a}

Calculating the numerical value, obtain:


d=33223=181.5md = \dfrac{33^2}{2\cdot3} = 181.5m

Answer. The runway is 181.5 m.


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