Question

question 29
2 points
a landing airplane makes contact with the runway with a speed of 75.0 m/s and moves toward the south. after 18.5 seconds, the airplane comes to rest. what is the average acceleration of the airplane during the landing?
12.3 m/s² north
4.05 m/s² north
2.11 m/s² north
2.11 m/s² south
4.05 m/s² south

Explanation:

Step1: Recall the formula for acceleration

The formula for average acceleration is \(a=\frac{v - v_0}{t}\), where \(v\) is the final velocity, \(v_0\) is the initial velocity, and \(t\) is the time.

Step2: Assign values to the variables

Given \(v_0 = 75.0\,\text{m/s}\) (south - we can take south as the positive direction for now, but we'll check the direction at the end), \(v=0\,\text{m/s}\), and \(t = 18.5\,\text{s}\).
Substitute into the formula: \(a=\frac{0 - 75.0}{18.5}\)

Step3: Calculate the acceleration

\(a=\frac{- 75.0}{18.5}\approx - 4.05\,\text{m/s}^2\). The negative sign indicates that the acceleration is in the opposite direction of the initial velocity. Since the initial velocity was south, the acceleration is north.

Answer:

\(4.05\,\text{m/s}^2\) north (the second option)