The plane takes 4.76 s to reach the end of the runway
Explanation:
The motion of the airplane is a uniformly accelerated motion (=at constant acceleration), therefore we can solve the problem by using the following suvat equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
where
s is the distance covered
u is the initial velocity
t is the time elapsed
a is the acceleration
In this problem, we have:
s = 102 m is the lenght of the runway
u = 0 is the initial velocity of the airplane
[tex]a=9.0 m/s^2[/tex] is its acceleration
Solving for t, we find the time needed to reach the end of the runway:
[tex]t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2(102)}{9.0}}=4.76 s[/tex]
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