Question

Determine the acceleration of the plane and time it takes.

Answer 1

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.

`v^2_f=v^2_0+2ad`

Where v_0 = 0, v_f = 81.0 m/s, and d = 1428m. Solve for a.

`\begin{gathered} (81\cdot(m)/(s))^2=0^2_{}+2a(1428m) \\ 6561\cdot(m^2)/(s^2)=2856m\cdot a \\ a=(6561\cdot(m^2)/(s^2))/(2856m) \\ a\approx2.30\cdot(m)/(s^2) \end{gathered}`

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.

`v_f=v_0+at`

Solve for t.

`\begin{gathered} 81\cdot(m)/(s)=0+2.3\cdot(m)/(s^2)\cdot t \\ t=(81\cdot(m)/(s))/(2.3\cdot(m)/(s^2)) \\ t\approx35.2s \end{gathered}`

The time elapsed is 35.2 seconds.

Therefore, the correct answer is the second option.