The airplane travels along a straight runway with an acceleration described by t

Question

The airplane travels along a straight runway with an acceleration described by the graph. It it starts from rest and requires a velocity of 90 m/s to take off, determine the minimum length of runway required and the time t' for take off. Construct the v-t and s-t graph.

Explanation / Answer

t < 10 s: initial v = 0 acceleration a = 0.8t = dv/dt v = integral of 0.8t dt = 0.4t^2 (note t = 0, v = 0) final v = 0.4*10^2 = 40 m/s v = 0.4t^2 = dx/dt x = integral of 0.4t^2 dt = 0.4t^3/3 (note t = 0, x = 0) displacement x1 = 0.4*10^3/3 = 133 m t > 10 s: initial velocity v = 40 m/s acceleration a = 8 m/s^2 final velocity v' = 90 m/s time t2 = (90 - 40)/8 = 50/8 = 6.25 s displacement x2 = vt2 + at2^2/2 = 406 m total displacement = x1 + x2 = 539 m total time = 10 + t2 = 16.25 s

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