an aeroplane touches down on the landing strip at an airpot.Assume that the speed at which the plane touches down is 100m.s and that the maximum length of the runway is 1000m.calculate the average acceleration that the plane must stop within the length of the runway
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To calculate the average acceleration that the plane must undergo in order to stop within the length of the runway, we can use the equation:
Acceleration = (Final Velocity - Initial Velocity) / Time
In this case, the final velocity is 0 m/s because the plane needs to come to a stop. The initial velocity is 100 m/s, and the distance traveled is 1000 m.
First, we need to find the time it takes for the plane to stop. We can use the equation of motion:
Displacement = (Initial Velocity + Final Velocity) / 2 * Time
Substituting the known values:
1000 m = (100 m/s + 0) / 2 * Time
Simplifying the equation:
1000 m = 50 m/s * Time
Dividing both sides of the equation by 50 m/s:
Time = 20 seconds
Now that we have the time, we can calculate the average acceleration:
Acceleration = (Final Velocity - Initial Velocity) / Time
Acceleration = (0 m/s - 100 m/s) / 20 s
Acceleration = -100 m/s / 20 s
Acceleration = -5 m/s²
Therefore, the average acceleration that the plane must undergo to stop within the length of the runway is -5 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, which is necessary for the plane to come to a stop.