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A plane starting at rest from one end of the runway undergoes a uniform acceleration of 4.8 m/s² for 15 seconds before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to takeoff?

Respuesta :

Starting from rest and accelerating at 4.8 m/s², the plane's velocity at time t is

v(t) = (4.8 m/s²) t

so that after 15 s, its speed at takeoff be

v(15 s) = (4.8 m/s²) * (15 s) = 72 m/s

In this time it takes for the plane to take off, it will travel a distance at time t of

x(t) = 1/2 (4.8 m/s²) t²

and it takes 15 s to take off, so the runway would have to have a length of

x(15 s) = 1/2 (4.8 m/s²) * (15 s)² = 540 m