Question

An airplane flies eastward and always accelerates at a constant rate. at one position along its path it has a velocity of 26.3 m/s, it then flies a further distance of 48100 m and afterwards its velocity is 41.9 m/s. find the airplane\'s acceleration and calculate how much time elapses while the airplane covers those 48100 m.

Answer 1

The airplane's acceleration is 0.47 m/s^2 and it takes approximately 32.4 seconds to cover the given distance.

Step-by-step explanation:

To find the airplane's acceleration, we can use the equation:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Plugging in the given values, we have:
(41.9 m/s)^2 = (26.3 m/s)^2 + 2a(48100 m)
Simplifying the equation, we find that the acceleration is 0.47 m/s^2.

To calculate the time elapsed, we can use the equation:
v = u + at
Plugging in the values, we have:
41.9 m/s = 26.3 m/s + 0.47 m/s^2 * t
Simplifying the equation, we find that t is approximately 32.4 seconds.

Answer 2

We will use the formula / equation to determined the time.

Distance = ½ * (vi + vf) * t
48100 = ½ * (26.3 + 41.9) * t
t = 48100 ÷ 34.1 = 1410.557185 seconds

We will use the formula / equation to determined the acceleration.

vf = vi + a * t
41.9 = 26.3 + a * 1410.557185
a = (41.9 – 26.3) ÷ 1410.557185 = 0.011059459 m/s^2

We will use the formula / equation to determined the acceleration.

vf^2 = vi^2 + 2 * a * d
41.9^1 = 26.3^2 + 2 * a * 48100
a = (41.9^2 – 26.3^2) ÷ 96200 = 0. 011059459 m/s^2
Since both answers are the same, I believe the acceleration is correct.