1) Acceleration: ![7.5 m/s^2](https://tex.z-dn.net/?f=7.5%20m%2Fs%5E2)
The motion of the plane is a uniformly accelerated motion, so we can find its acceleration by using the suvat equation
![v^2-u^2=2as](https://tex.z-dn.net/?f=v%5E2-u%5E2%3D2as)
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the displacement
Here we have
v = 150 m/s is the final velocity of the plane
u = 0 (it starts from rest)
a=?
s = 1500 m is the displacement
Solving for a, we find
![a=\frac{v^2-u^2}{2s}=\frac{150^2-0}{2(1500)}=7.5 m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%5E2-u%5E2%7D%7B2s%7D%3D%5Cfrac%7B150%5E2-0%7D%7B2%281500%29%7D%3D7.5%20m%2Fs%5E2)
2. Time: 20 s
For this part of the problem, we can use another suvat equation:
![v=u+at](https://tex.z-dn.net/?f=v%3Du%2Bat)
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
Here we already know:
v = 150 m/s is the final velocity of the plane
u = 0 (it starts from rest)
(found in part 1)
Solving for t, we find the time taken for the plane to reach the final velocity of 150 m/s:
![t=\frac{v-u}{a}=\frac{150-0}{7.5}=20 s](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bv-u%7D%7Ba%7D%3D%5Cfrac%7B150-0%7D%7B7.5%7D%3D20%20s)