An airplane flies eastward and always accelerates at a constant rate. At one position along its path it has a velocity of 34.3 m/s, it then flies a further distance of 40100 m and afterwards its velocity is 47.5 m/s. Find the airplane/'s acceleration and calculate how much time elapses while the airplane covers those 40100 m.

We'll need two equations.

v² = v₀² + 2a (x - x₀)

where v is the final velocity, v₀ is the initial velocity, a is the acceleration, x is the final position, and x₀ is the initial position.

x = x₀ + ½ (v + v₀) t

where t is time.

Given:

v = 47.5 m/s

v₀ = 34.3 m/s

x - x₀ = 40100 m

Find: a and t

(47.5) ² = (34.3) ² + 2a (40100)

a = 0.0135 m/s²

40100 = ½ (47.5 + 34.3) t

t = 980 s