**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:*- ○ \(37.0 \, \text{m/s}\)- ○ \(103.9 \, \text{m/s}\)- ○ \(65.7 \, \text{m/s}\)- ○ \(93.0 \, \text{m/s}\)- ○ \(186 \, \text{m/s}\)---### Solution ApproachTo 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 \(103.9 \, \text{m/s}\).---**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.

Name: **Understanding Acceleration and Final Speed***Problem Statement:*An
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: **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:*- ○ \(37.0 \, \text{m/s}\)- ○ \(1