To find the initial velocity of the airplane when it first began to decelerate, we can use the equations of motion. In this case, we can use the following equation:
\[ v^2 = u^2 + 2as \]
Where:
- \( v \) = final velocity (0 m/s, since the airplane comes to rest)
- \( u \) = initial velocity (what we're trying to find)
- \( a \) = acceleration (which will be negative since it's deceleration, so we use -3.0 m/s\(^2\))
- \( s \) = distance (1,300 m)
Rearranging the equation to solve for \( u^2 \):
\[ 0 = u^2 + 2(-3.0)(1300) \]
This simplifies to:
\[ 0 = u^2 - 7800 \]
Now, we can solve for \( u^2 \):
\[ u^2 = 7800 \]
Taking the square root to find \( u \):
\[ u = \sqrt{7800} \]
Calculating the square root:
\[ u \approx 88.37 , \text{m/s} \]
Therefore, the velocity of the airplane when the acceleration first began was approximately 88.37 m/s.
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