An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.
To find the distance traveled, we can use the kinematic equation:
\[d = v_i t + \frac{1}{2} a t^2\]
Where:
\(d\) = distance traveled
\(v_i\) = initial velocity = 0 m/s
\(a\) = acceleration = 3.20 m/s²
\(t\) = time taken = 32.8 s
Plugging in the values, we get:
\[d = (0)(32.8) + \frac{1}{2} (3.20)(32.8)^2\]
\[d = 0 + \frac{1}{2} (3.20)(1075.84)\]
\[d = 0 + 1721.344\]
\[d ≈ 1721.344 m\]
Therefore, the distance traveled before takeoff is approximately 1721.344 meters.