# PhysicsAlgebra/Physics problem - kinematics

#### mathkid3

##### New member
A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?

so, I am new to kinomatic equations. We are using the 4 Basic ones.

need to see this one worked out if I may.

Thanks

#### Ackbach

##### Indicium Physicus
Staff member
Re: Algebra/Physics problem

What is the target variable? That is, what is it for which you're trying to solve?

#### mathkid3

##### New member
Re: Algebra/Physics problem

distance?

#### MarkFL

Staff member
Re: Algebra/Physics problem

What is it that you are given? And how may we relate these values?

#### Ackbach

##### Indicium Physicus
Staff member
Re: Algebra/Physics problem

Another way of saying what MarkFL said is this: can you write down a relevant, correct equation involving the target variable of distance?

#### wittysoup

##### New member
Re: Algebra/Physics problem

A light plane must reach a speed of 33 m/s for takeoff. How long must the runway be if the plane has a constant acceleration of 3.8 m/s2 ?

so, I am new to kinomatic equations. We are using the 4 Basic ones.

need to see this one worked out if I may.

Thanks
I think the OP meant the kinematic equations, 4 basic ones meaning:

1) x=x0+V0t+1/2at2
2) V=V0+at
3) a=constant
4) V2=V02+2a(x-x0)

If this is the case, the answer is a matter of determining starting values.

We can assume that the plane starts off at point 0 on the runway meaning that x0=0. we can also assume that the plane's initial velocity is 0, V0=0 (before moving). now we are given the acceleration, a=3.8m/s2, and final velocity, V=33m/s. From this we can find how long it will take the plane to reach the final velocity, using equation 2:

33m/s=0+(3.8m/s2)t
t=(33/3.8)s

Now that we have a value for t, we can use equation 1 to find the total runway length, x, required to reach takeoff speed:

x=0+0(t)+1/2at2
=(1/2)(3.8m/s2)((33/3.8)s)2
=143.30m

therefore the minimum amount of runway needed to reach the plane's necessary takeoff speed is 143.30 meters.