An aircraft starts from rest and accelerates at 42.5m/s^2 until it takes off at the end of the runway. How long will it take the aircraft to travel down the 2.6km runway?
Answer is 11 seconds
km -> m
a=v²/2s
s=at²/2
t=sqrt(2s/a)
11 s
To find the time it takes for the aircraft to travel down the runway, we can use the equation:
\[ d = \frac{1}{2}at^2 \]
where:
d = distance traveled (2.6 km = 2600 m)
a = acceleration (42.5 m/s^2)
t = time
We need to rearrange the equation to solve for t:
\[ t^2 = \frac{2d}{a} \]
Substituting the given values, we get:
\[ t^2 = \frac{2 \times 2600}{42.5} \]
\[ t^2 = \frac{5200}{42.5} \]
\[ t^2 = 122.35 \]
Taking the square root of both sides, we find:
\[ t = \sqrt{122.35} \]
\[ t \approx 11 \text{ seconds} \]
Therefore, it will take approximately 11 seconds for the aircraft to travel down the 2.6 km runway.