To determine the time it would take for a plane to reach the speed of sound, we need to convert the units to ensure consistency. The speed of sound is commonly expressed in meters per second, so we'll convert the acceleration rate to meters per second squared.
Given: Acceleration = 10 miles per hour per second
To convert miles per hour to meters per second, we'll use the following conversion factors: 1 mile = 1609.34 meters 1 hour = 3600 seconds
Converting the acceleration rate: Acceleration = 10 miles per hour per second = 10 * 1609.34 meters / 3600 seconds ≈ 4.47 meters per second squared
Now, let's calculate the time it takes for the plane to reach the speed of sound.
The speed of sound is approximately 343 meters per second.
Using the formula of motion: v = u + at
Where: v = final velocity (speed of sound) = 343 m/s u = initial velocity (0 m/s, starting from rest) a = acceleration = 4.47 m/s² t = time (unknown)
Substituting the known values into the equation: 343 = 0 + 4.47t
Simplifying the equation: 4.47t = 343 t = 343 / 4.47 t ≈ 76.8 seconds
Therefore, it would take approximately 76.8 seconds for the plane to reach the speed of sound if it starts from rest and accelerates at a rate of ten miles per hour every second.