The takeoff speed for a Boeing 737 is about 250 km/h. It reaches its takeoff speed after 50 seconds. What is its acceleration?
The Correct Answer and Explanation is :
To determine the acceleration of the Boeing 737, we can use the formula for acceleration:
[
a = \frac{{v – u}}{{t}}
]
where:
- ( v ) is the final velocity (takeoff speed of 250 km/h, which we need to convert to meters per second),
- ( u ) is the initial velocity (0, assuming it starts from rest),
- ( t ) is the time taken to reach the takeoff speed (50 seconds).
Step 1: Convert the Final Velocity
Since acceleration is typically expressed in meters per second squared, we need to convert 250 km/h to meters per second.
[
250 \, \text{km/h} = 250 \times \frac{1000}{3600} = 69.44 \, \text{m/s}
]
Step 2: Plug Values into the Formula
Now that we have:
- ( v = 69.44 \, \text{m/s} )
- ( u = 0 \, \text{m/s} )
- ( t = 50 \, \text{s} )
we can substitute these values into the formula:
[
a = \frac{{69.44 – 0}}{{50}} = 1.39 \, \text{m/s}^2
]
Explanation
The acceleration of an object tells us how quickly it changes its speed over a certain period. In this case, the Boeing 737 starts from a stationary position (0 m/s) and needs to reach 250 km/h (69.44 m/s) in order to take off. By dividing the change in speed by the time it takes to reach that speed, we calculate how much the speed increases every second, which is the acceleration.
The calculated acceleration of 1.39 m/s² means that every second, the Boeing 737’s speed increases by 1.39 meters per second until it reaches the necessary takeoff speed of 250 km/h. This acceleration value is crucial for the aircraft to achieve lift, overcoming gravity and achieving flight. Without reaching this acceleration, the plane might not attain sufficient speed, which could prevent a successful takeoff.