Question

An airplane is taxiing onto the runway at 10 meters per second. If it accelerates steadily at 3 meters per second squared and its takeoff speed is 90 meters per second, how long will it take for the plane to reach takeoff speed?

Answer 1

To find out how long it will take for the airplane to reach its takeoff speed, we can use the equation of motion which relates initial speed, acceleration, final speed, and time.

The formula is:

\[
v = u + at
\]

where:
- \( v \) is the final velocity (takeoff speed),
- \( u \) is the initial velocity (taxiing speed),
- \( a \) is the acceleration, and
- \( t \) is the time.

Given:
- \( u = 10 \) m/s (initial speed)
- \( v = 90 \) m/s (takeoff speed)
- \( a = 3 \) m/s² (acceleration)

We need to solve for \( t \):

1. Substitute the values into the equation:

\[
90 = 10 + 3t
\]

2. Rearrange the equation to solve for \( t \):

\[
90 - 10 = 3t
\]
\[
80 = 3t
\]
\[
t = \frac{80}{3}
\]

3. Calculate \( t \):

\[
t \approx 26.67 \text{ seconds}
\]

Therefore, it will take approximately **26.67 seconds** for the airplane to reach its takeoff speed.