A plane accelerates from rest at a constant rate of 5.00 m/s2 along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time tTO needed to take off?
To find the time required for the plane to take off, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (takeoff velocity)
u = initial velocity (0 m/s, as the plane starts from rest)
a = acceleration (5.00 m/s^2)
t = time
Final velocity (v) can be calculated using another kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (takeoff velocity)
u = initial velocity (0 m/s)
a = acceleration (5.00 m/s^2)
s = distance (1800 m)
Rearranging the equation to solve for v:
v^2 = 0 + 2(5.00)(1800)
v^2 = 2(5.00)(1800)
v^2 = 18000
v = sqrt(18000)
v ā 134.16 m/s
Now, we can substitute the values into the first equation and solve for t:
134.16 = 0 + 5.00t
t = 134.16 / 5.00
t ā 26.83 seconds
Therefore, the time required for the plane to take off (tTO) is approximately 26.83 seconds.
To find the time required for takeoff, we can use the equation for uniformly accelerated motion:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the plane starts from rest, so the initial velocity (u) is 0 m/s. The acceleration (a) is given as 5.00 m/s^2. We want to find the time (t) it takes for the plane to reach the required takeoff velocity.
Since we know the acceleration and the displacement (runway length), we can use another equation for uniformly accelerated motion:
s = ut + (1/2)at^2
where:
s = displacement
In this case, the displacement (s) is given as 1800 m. Again, the initial velocity (u) is 0 m/s, and the acceleration (a) is 5.00 m/s^2. We want to find the time (t) it takes for the plane to cover this distance.
Rearranging the equation for displacement, we get:
t^2 = 2s / a
Substituting the values, we have:
t^2 = 2 * 1800 m / 5.00 m/s^2
t^2 = 720
Taking the square root of both sides, we find:
t ā 26.87 seconds (rounded to two decimal places)
Therefore, the time required for takeoff (tTO) is approximately 26.87 seconds.
you want t when
2.5t^2 = 1800