Question

A plane accelerates from rest at a constant rate of 5.00 m/s2 along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time tTO needed to take off? Express your answer in seconds using three significant figures.

Answer 1

26.8 seconds

Step-by-step explanation:

To solve this problem we have to use 2 kinematics equations: *I can't use subscripts for some reason on here so I am going to use these variables:

v = final velocity

z = initial velocity

x = distance

t = time

a = acceleration

`{v}^(2) = {z}^(2) + 2ax`

`v = z + at`

First let's find the final velocity the plane will have at the end of the runway using the first equation:

`{v}^(2) = {0}^(2) + 2(5)(1800)`

`v = 60 √(5)`

Now we can plug this into the second equation to find t:

`60 √(5) = 0 + 5t`

`t = 12 √(5)`

Then using 3 significant figures we round to 26.8 seconds