The equation of motion of the aircraft is given as s (t) = 1.8t ^ 2-0.02t ^ 2. The separation of the aircraft from

The equation of motion of the aircraft is given as s (t) = 1.8t ^ 2-0.02t ^ 2. The separation of the aircraft from the runway is carried out at the moment when the acceleration is equal to zero. Time required for take-off

These problems: S (t) – the equation of motion of the aircraft (S (t) = 1.8t ^ 2 – 0.02t ^ 3); a – acceleration at the moment of separation (a = 0 m / s2).

1) The equation of aircraft acceleration: a (t) = S (t) ” = (1.8t ^ 2 – 0.02t ^ 3) ” = (1.8 * 2 * t – 0.02 * 3 * t ^ 2) ‘= (3.6t – 0.06t ^ 2)’ = 3.6 * 1 – 0.06 * 2 * t = 3.6 – 0.12t.

2) Time for take-off: a (t) = 0 = 3.6 – 0.12t, whence t = 3.6 / 0.12 = 30 s.

Answer: The aircraft needs 30 seconds to accelerate.