Question

A Plane has a takeoff speed of 150 m/s and requires 1500m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed.

Answer 1

1) Acceleration: $7.5 m/s^2$

The motion of the plane is a uniformly accelerated motion, so we can find its acceleration by using the suvat equation

$v^2-u^2=2as$

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

$a=\frac{v^2-u^2}{2s}=\frac{150^2-0}{2(1500)}=7.5 m/s^2$

2. Time: 20 s

For this part of the problem, we can use another suvat equation:

$v=u+at$

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)

$a=7.5 m/s^2$ (found in part 1)

Solving for t, we find the time taken for the plane to reach the final velocity of 150 m/s:

$t=\frac{v-u}{a}=\frac{150-0}{7.5}=20 s$