Answer:
Approximately [tex]61\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
In this question, the following information about the motion is given:
The goal is to find the velocity [tex]v[/tex] after achieving the given displacement of [tex]x = 500\; {\rm m}[/tex]. Since the duration of the acceleration is neither given nor required, the SUVAT equation [tex]v^{2} - u^{2} = 2\, a\, x[/tex] would be the most suitable. Rearrange this equation to find [tex]v[/tex] in terms of [tex]u[/tex], [tex]a[/tex], and [tex]x[/tex]:
[tex]\displaystyle v^{2} = u^{2} + 2\, a\, x[/tex].
[tex]\begin{aligned} v &= \sqrt{u^{2} + 2\, a\, x} \\ &= \sqrt{(15\; {\rm m\cdot s^{-1}})^{2} + 2\, (3.5\; {\rm m\cdot s^{-2}})\, (500\; {\rm m})} \\ &\approx 61\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
In other words, the velocity of the aircraft at a displacement of [tex]x = 500\; {\rm m}[/tex] from the initial position would be [tex]v \approx 61\; {\rm m\cdot s^{-1}}[/tex].