MHB Algebra/Physics problem - kinematics

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To determine the runway length required for a light plane to reach a takeoff speed of 33 m/s with a constant acceleration of 3.8 m/s², the kinematic equations are applied. The initial velocity is assumed to be 0, and the time to reach the final velocity is calculated using the equation V = V0 + at, resulting in approximately 8.68 seconds. Using the equation for distance, x = x0 + V0t + 1/2at², the total runway length is computed to be 143.30 meters. This calculation confirms that a minimum runway length of 143.30 meters is necessary for the plane to achieve its required speed for takeoff. Understanding these kinematic equations is essential for solving similar physics problems.
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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
 
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Re: Algebra/Physics problem

What is the target variable? That is, what is it for which you're trying to solve?
 
Re: Algebra/Physics problem

distance?
 
Re: Algebra/Physics problem

What is it that you are given? And how may we relate these values?
 
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?
 
Re: Algebra/Physics problem

mathkid3 said:
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.
 
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