A light plane must reach a speed of 35 m/s for takeoff. How long a runaway is needed if the (constant) acceleration is $3.0 \textrm{ m/s}^2$?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. A good strategy for any question is to start by writing down the things that you know and then the thing that you wanna find. So the final speed of this plane has to be 35 meters per second; it starts from rest so its initial speed is zero; it has an acceleration of 3.0 meters per second squared and we want to find the length of the runway that it needs to travel along in order to reach this final speed given that acceleration. So because acceleration is constant, we can use all the formulas in this chapter and we have v f squared equals v i squared plus 2ad is gonna fit the bill because we know everything here except for the one thing d. We know the initial speed is zero so that term disappears the final speed we know and we are gonna divide both sides by 2a in order to solve for d; we'll also flip the sides around so the unknown is on the left. So d is final velocity squared divided by 2 times acceleration. So that's 35 meters per second squared divided by 2 times 3 meters per second squared and with two significant figures, we have 2.0 times 10 to the 2 meters or 200 meters is the required length of the runway.