Final answer:
The airplane was moving at a speed of 157.5 m/s when it took off, calculated using the formula for final velocity by plugging in the given constant acceleration of 4.50 m/s² and the time span of 35.0 seconds.
Step-by-step explanation:
Calculating the Takeoff Speed of an Airplane
An airplane starts from rest and accelerates down a runway with a constant acceleration. To find the speed when the airplane took off, we use the formula for calculating final velocity when initial velocity, acceleration, and time are known:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) × Time (t))
Since the airplane starts from rest, its initial velocity (u) is 0 m/s. Given the constant acceleration of 4.50 m/s² and the time span of 35.0 seconds before takeoff, we can plug these values into the formula to calculate its takeoff speed:
Final velocity = 0 m/s + (4.50 m/s² × 35.0 s)
By multiplying the acceleration by the time, we get:
Final velocity = 4.50 m/s² × 35.0 s = 157.5 m/s
This is the speed at which the airplane was moving when it took off.