Question

A light plane must reach a speed of 32m/s for takeoff How long a runway is needed if the (constant) acceleration is 2.9m/s2 ?
Express your answer using two significant figures.

Answer 1

The time t needed to accelerate to a speed of 32m/s can be found from the equation:
\[v=v _{0}+at\]
where
\[v _{0}\ is\ the\ initial\ speed\]
a is the acceleration and v is the speed at time t.
In this case we assume the initial speed is zero, therefore you just solve for t by substituting the given values in:
\[t=\frac{v}{a}\]
The average speed is found from the equation:
\[\bar{v}=\frac{v _{0}+v}{2}\]
When you have found the average speed and the time t, the required distance d is found from:
\[d=\bar{v} \times t\]