An airplane starts from rest and accelerates at 10.8 m/s?. What is its speed at the end of a 500 m-long runway? 37.0 m/s 103.9 m/s O 65.7 m/s 93.0 m/s O 186 m/s
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
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.
![**Understanding Acceleration and Final Speed**
*Problem Statement:*
An airplane starts from rest and accelerates at \(10.8 \, \text{m/s}^2\). What is its speed at the end of a \(500 \, \text{m}\)-long runway?
*Options:*
- ○ \(37.0 \, \text{m/s}\)
- ○ \(103.9 \, \text{m/s}\)
- ○ \(65.7 \, \text{m/s}\)
- ○ \(93.0 \, \text{m/s}\)
- ○ \(186 \, \text{m/s}\)
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### Solution Approach
To find the final speed (\(v\)) of the airplane at the end of the runway, we can use the kinematic equation:
\[ v^2 = u^2 + 2as \]
where:
- \( u \) is the initial velocity (which is \(0 \, \text{m/s}\) since the plane starts from rest),
- \( a \) is the acceleration (\(10.8 \, \text{m/s}^2\)),
- \( s \) is the displacement (length of the runway, \(500 \, \text{m}\)).
Plugging in the values:
\[ v^2 = 0 + 2 \cdot 10.8 \, \text{m/s}^2 \cdot 500 \, \text{m} \]
\[ v^2 = 10800 \, \text{m}^2/\text{s}^2 \]
\[ v = \sqrt{10800} \, \text{m/s} \]
\[ v \approx 103.9 \, \text{m/s} \]
Thus, the correct option is \(103.9 \, \text{m/s}\).
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**Learning Points:**
- This problem helps understand how to apply kinematic equations to calculate the final velocity of an object when given initial velocity, acceleration, and distance.
- This exercise emphasizes the importance of understanding motion under constant acceleration and how to manipulate the kinematic equations accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb00ff254-c89e-4d98-9f37-4465f02914e3%2F62cb3ff9-b26a-4818-9f86-5eba92823c02%2Fb9zmwoc_processed.jpeg&w=3840&q=75)
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