Answer to Question #125353 in Physics for Josh

Question

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?

Answer 1

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

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

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

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

Substituting the expression for $t$ into the last formula, get:

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

Calculating the numerical value, obtain:

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

Answer. The runway is 181.5 m.