an euler airline flight is getting ready to take off. gary mcdonald the pilot starts from rest at the edge of the runway. he needs to accelerate to a speed of 300km/hr in 30 sec. acceleration is defined as the change in speed per unit time. what is gary’s average acceleration in meters per second per second which is equivalent to meters per second squared during take off.
(300000 m/hr / 3600 s/hr) / 30 s
To find Gary's average acceleration during takeoff, we need to use the given information about the change in speed and time. Here's how we can calculate it:
1. Convert the speed from km/hr to m/s:
300 km/hr * (1000 m / 1 km) * (1 hr / 3600 s) = 83.33 m/s
2. Convert the time from seconds to hours:
30 sec * (1 min / 60 sec) * (1 hr / 60 min) = 0.00833 hr
3. Use the formula for average acceleration:
Average Acceleration (a) = (Final Velocity - Initial Velocity) / Time
Initial Velocity (u) is 0 m/s (since Gary starts from rest).
Final Velocity (v) is 83.33 m/s (the desired speed).
Time (t) is 0.00833 hr.
Average Acceleration (a) = (83.33 m/s - 0 m/s) / 0.00833 hr
4. Convert the time from hours to seconds:
0.00833 hr * (3600 s / 1 hr) = 30 s
Average Acceleration (a) = 83.33 m/s / 30 s
5. Calculate for average acceleration:
Average Acceleration (a) = 2.78 m/s²
Therefore, Gary's average acceleration during takeoff is 2.78 m/s².