A model airplane is flying north at 12.5 m/s initially, and 25 seconds later is observed heading 30 degrees west of north at 25 m/s. What is the magnitude of the average acceleration during this time interval? A) 0.37 m/s² B) 0.50 m/s² C) 0.62 m/s² D) 0.87 m/s²

Question

Quizplus · Accepted Answer

To find the average acceleration, we need to calculate the change in velocity and divide it by the time interval.

First, we need to find the components of the initial and final velocities in the north and west directions.

Initial velocity: 
North component = 12.5 m/s 
West component = 0 m/s

Final velocity: 
North component = 25 m/s * sin(30°) ≈ 12.5 m/s 
West component = -25 m/s * cos(30°) ≈ -21.7 m/s

The change in velocity in the north direction is Δv = 12.5 m/s - 12.5 m/s = 0 m/s 
The change in velocity in the west direction is Δv = -21.7 m/s - 0 m/s = -21.7 m/s

The time interval is 25 seconds.

So the average acceleration is:

a = Δv / Δt

a = (-21.7 m/s) / (25 s)

a ≈ -0.87 m/s^2

Note that the negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which makes sense since the plane is slowing down and changing direction.

The magnitude of the average acceleration is |a| = 0.87 m/s^2, which is closest to choice C, 0.62 m/s^2.

A Model Airplane Is Flying North at 12