We know that
• The final velocity is 81.0 m/s.
,
• The distance traveled is 1428 m.
,
• The initial velocity is zero.
First, find the acceleration using a formula that relates final velocity, initial velocity, acceleration, and distance.
[tex]v^2_f=v^2_0+2ad[/tex]
Where v_0 = 0, v_f = 81.0 m/s, and d = 1428m. Solve for a.
[tex]\begin{gathered} (81\cdot\frac{m}{s})^2=0^2_{}+2a(1428m) \\ 6561\cdot\frac{m^2}{s^2}=2856m\cdot a \\ a=\frac{6561\cdot\frac{m^2}{s^2}}{2856m} \\ a\approx2.30\cdot\frac{m}{s^2} \end{gathered}[/tex]
The acceleration of the plane is 2.30 m/s^2.
To find the time elapsed, use a formula that relates final velocity, initial velocity, acceleration, and time.
[tex]v_f=v_0+at[/tex]
Solve for t.
[tex]\begin{gathered} 81\cdot\frac{m}{s}=0+2.3\cdot\frac{m}{s^2}\cdot t \\ t=\frac{81\cdot\frac{m}{s}}{2.3\cdot\frac{m}{s^2}} \\ t\approx35.2s \end{gathered}[/tex]
The time elapsed is 35.2 seconds.
Therefore, the correct answer is the second option.
