Acertain aircraft has a liftoff speed of 121 km/h. (a) what minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 295 m? (b) how long does it take the aircraft to become airborne?

A) The minimum constant acceleration is

B) The airplane takes 17.553 seconds to become airborne.

Explanation:

First, consider the basic equations for the motion with constant acceleration:

Where and are the initial position and velocity respectively; a is the acceleration and t the time.

Let's imagine that the aircraft had become airborne after the 295 m run, and let's model this movement by the last equations. The airplane is considered to be at position zero ( and start from repose (it's start velocity is zero: )

Let's convert the velocity to m/s:

The airplane has a velocity of 33.611 m/s and has run 295 meters when it becomes airborne, so at that time:

(The initial velocity is zero)

(The initial position is zero)

At this point we have a two-variable-two-equation system; if we could solve it we would know the time and the acceleration.

Let's isolate the time from the first equation and replace it in the second one.

Then, find the acceleration:

Now, it is possible to find the time by means of any of the initial equations we wrote. Let's take, for example, the first one: