Question

10 points



Question at position 2

An airplane accelerates from rest down a runway at 9.47 m/s2 for 26.3 seconds until it lifts off the ground.

Determine the Distance traveled before takeoff.


15,507.8 m


15,507.8 m/s


3,275.15 m/s


3,275.15 m

Answer 1

To determine the distance traveled before takeoff, you can use the kinematic equation for distance when starting from rest:

\[
d = v_i t + \frac{1}{2} a t^2
\]

where:
- \( d \) = distance traveled
- \( v_i \) = initial velocity (0 m/s, since the airplane starts from rest)
- \( a \) = acceleration (9.47 m/s²)
- \( t \) = time (26.3 seconds)

Since the initial velocity \( v_i = 0 \):

\[
d = 0 \cdot t + \frac{1}{2} a t^2
\]
\[
d = \frac{1}{2} (9.47 \, \text{m/s}^2) (26.3 \, \text{s})^2
\]

Calculating \( (26.3 \, \text{s})^2 \):

\[
(26.3)^2 = 691.69 \, \text{s}^2
\]

Now substitute this back into the distance formula:

\[
d = \frac{1}{2} \times 9.47 \, \text{m/s}^2 \times 691.69 \, \text{s}^2
\]
\[
d = 4.735 \times 691.69
\]
\[
d \approx 3275.15 \, \text{m}
\]

Thus, the distance traveled before takeoff is approximately **3275.15 m**. Therefore, the correct answer is:
**3,275.15 m**.