Ch1 Ex 1b Q5 Starting from rest, an aircraft accelerates to its take-off speed of 60 m/s …

The Problem:

Starting from rest, an aircraft accelerates to its take-off speed of 60 m s1 in a distance of 900 metres. Assuming constant acceleration, find how long the take-off run lasts. Hence calculate the acceleration.

Title: Soaring to Take-Off: Aircraft Acceleration Odyssey

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Douglas Quadling Mechanics 1
Exercise 1B Q5

Problem Statement

Starting from rest, an aircraft accelerates to its take-off speed of 60 m/s in a distance of 900 meters. Assuming constant acceleration, find:

1. How long the take-off run lasts.
2. The acceleration of the aircraft.

Solution

Given:

• Initial velocity (u) = 0 m/s (starting from rest)
• Final velocity (v) = 60 m/s
• Distance (s) = 900 meters
• Acceleration (a) = constant (to be calculated)
• Time (t) = to be calculated

Step 1: Find the Time (t) for the Take-Off Run

We use the equation of motion:

s = (u + v) / 2 * t

Substitute the values:

900 = (0 + 60) / 2 * t
900 = 30 * t
t = 900 / 30
t = 30 seconds

Time for the take-off run = 30 seconds

Step 2: Calculate the Acceleration (a)

We use the equation of motion:

v = u + a * t

Substitute the values:

60 = 0 + a * 30
a = 60 / 30
a = 2 m/s²

Acceleration of the aircraft = 2 m/s²

Final Answers:

1. Time for the take-off run = 30 seconds
2. Acceleration of the aircraft = 2 m/s²