Problem 8 - airplane acceleration

An airplane must reach a speed of 350 km/h on the runway for takeoff. What is the minimum acceleration required for takeoff from a 2.0 km long runway? What is the time used for reaching this speed?

v_T = 350 km/h    - speed required for takeoff
L_r = 2.0 km - length of the runway
a = ? - minimum acceleration required
t = ? - time required to reach this speed.

On the basis of equations describing linear motion with constant acceleration we can write

L_r = (1/2)at² v_T = at This is a set of two linear equations with solutions a = (1/2)v²/ L_r t = 2L_r / v
Substituting numbers given in the problem, we get
a = 2.36 m/s²
t = 41.14 s

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