Analyze the Acceleration of an Airplane During Takeoff

Calculating the Acceleration of an Airplane

An airplane reaches a velocity of 71 m/s when it takes off. If the runway is 1.0 km long, what must its acceleration be?

Final answer:

To find the acceleration of the airplane, use the formula: Acceleration = (Final velocity - Initial velocity) / Time.

Given that the runway is 1.0 km long and the airplane reaches a velocity of 71 m/s, convert the runway length to meters and calculate the time it takes for the airplane to reach that velocity. Finally, use the time to find the acceleration, which is 5.05 m/s².

Explanation:

In order to find the acceleration of the airplane, we need to use the formula:

Acceleration = (Final velocity - Initial velocity) / Time

Since we have the final velocity (71 m/s) and the runway length (1.0 km), we can use the formula to find the time it takes for the airplane to reach that velocity. Then, we can use the time to find the acceleration.

Let's convert the runway length to meters: 1.0 km = 1000 m. Now, we can use the formula:

Time = Distance / Velocity

Substituting the values, we get:

Time = 1000 m / 71 m/s = 14.08 s

Finally, we can use the time to find the acceleration:

Acceleration = (Final velocity - Initial velocity) / Time = (71 m/s - 0 m/s) / 14.08 s = 5.05 m/s²