Question

The minimum takeoff speed for a certain airplane is 75 m/s. What minimum acceleration is required if the plane must leave a runway of length 1050 m? Assume plane starts at rest.

A) 1.5 m/s^2
B) 3.0 m/s^2
C) 4.5 m/s^2
D) 6.0 m/s^2
E) 2.7 m/s^2

Answer 1

The minimum acceleration required for an airplane to reach a takeoff speed of 75 m/s on a runway of 1050 m is 2.7 m/s^2, using the kinematic equation for constant acceleration.

Step-by-step explanation:

The question concerns the minimum acceleration required for an airplane to take off from a runway of a specific length. Given that the airplane must reach a takeoff speed of 75 m/s over a distance of 1050 m, starting from rest, we can use the kinematic equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance covered.

With the initial velocity u = 0 (starting from rest) and rearranging the formula to solve for the acceleration a, you get a = v^2 / (2s). Plugging in the values, the calculation becomes a = (75 m/s)^2 / (2 × 1050 m), which simplifies to a = 5625 m^2/s^2 / 2100 m = 2.7 m/s^2.

Therefore, the minimum acceleration required is 2.7 m/s^2, which corresponds to option E.