An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.8 m?
An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.8 m?
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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![**Question:**
An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.8 m?
**Explanation:**
This problem involves calculating the minimum time required for an aircraft to become airborne given the distance of the takeoff run and the lift-off speed, assuming constant acceleration.
To solve problems like this, physics principles such as kinematic equations are used, particularly those that relate motion with constant acceleration. Here are the steps and formulae involved:
1. **Convert lift-off speed to m/s:**
\( 12.1 \text{ km/h} = \frac{12.1 \times 1000}{3600} \text{ m/s} \)
2. **Use the second kinematic equation:**
\[ s = ut + \frac{1}{2}at^2 \]
- Where \( s \) is the displacement (23.8 m),
- \( u \) is the initial velocity (0 m/s, assuming the aircraft starts from rest),
- \( a \) is the constant acceleration,
- \( t \) is the time.
3. **Rearrange for time \( t \):**
- Since initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2}at^2 \]
- Find \( t \) by solving the quadratic equation.
If given the acceleration \( a \), substitute to find \( t \).
To determine the detailed solution and the exact value of \( t \), further calculations or the given acceleration value would be necessary. This step-by-step method demonstrates the application of kinematic equations to practical problems in aeronautics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f0c4e77-fecd-4d18-90ed-9b329310f28f%2F7989968f-87ab-4f3a-868f-a26ab7d95f2d%2Fjgevti.png&w=3840&q=75)
Transcribed Image Text:**Question:**
An aircraft has a lift-off speed of 12.1 km/h. If the aircraft's acceleration is constant, what minimum time is required for the aircraft to be airborne after a takeoff run of 23.8 m?
**Explanation:**
This problem involves calculating the minimum time required for an aircraft to become airborne given the distance of the takeoff run and the lift-off speed, assuming constant acceleration.
To solve problems like this, physics principles such as kinematic equations are used, particularly those that relate motion with constant acceleration. Here are the steps and formulae involved:
1. **Convert lift-off speed to m/s:**
\( 12.1 \text{ km/h} = \frac{12.1 \times 1000}{3600} \text{ m/s} \)
2. **Use the second kinematic equation:**
\[ s = ut + \frac{1}{2}at^2 \]
- Where \( s \) is the displacement (23.8 m),
- \( u \) is the initial velocity (0 m/s, assuming the aircraft starts from rest),
- \( a \) is the constant acceleration,
- \( t \) is the time.
3. **Rearrange for time \( t \):**
- Since initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2}at^2 \]
- Find \( t \) by solving the quadratic equation.
If given the acceleration \( a \), substitute to find \( t \).
To determine the detailed solution and the exact value of \( t \), further calculations or the given acceleration value would be necessary. This step-by-step method demonstrates the application of kinematic equations to practical problems in aeronautics.
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