# An airplane accelerates down a runway at 3.20 m/s_2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff?

##### 2 Answers

Distance traveled

or

#### Explanation:

**Aide memoires**

There are three equations for 1D motion involving constant acceleration.

#v=u+a t# #s=ut+1/2at^2# #v^2-u^2=2as#

where symbols have meanings ascribed to each.

In the problem given quantities are acceleration

Inspection reveals that equation 2 is the most suitable as it has all three quantities of interest in it except initial velocity

Answer starts from here

We know that

where

Now we assume that the airplane starts from rest on the runway. Therefore, first term on the RHS is zero. Inserting given values in the equation

Supplementary answer below.

#### Explanation:

(i) Let

Acceleration is rate of change of velocity,

You obtain first equation.

(ii) Once we know the initial velocity and final velocity

Average velocity

Distance

Insert the value of

You obtain second equation.

(iii) Eliminate time

taking

Insert

You get the third one as

**Above equation is direct outcome of the Law of Conservation of Energy** .

Change in kinetic energy

#="Final KE"-"Initial KE"#

#=># Change in kinetic energy#=1/2mv^2-1/2m u^2# ..........(B)

Work done by a constant force

#W=vecFcdotvecs#

Rewriting it in terms of acceleration we get

#W=(mveca)cdot vecs#

As direction of force/acceleration and motion is same, we get

#W=mas# ...........(C)

Using Law of Conservation of energy

Change in kinetic energy

#=W#

#:.1/2mv^2-1/2m u^2=mas#

#=>color(blue)(v^2-u^2=2as)#

Another thing one must remember that even though it is not written explicitly, in all above equations, symbols