Kinematic Equations Rearrangment

[Malelia123]

Homework Statement

A= Acceleration
Vf = Final Velocity
Vi = Initial Velocity
D= Displacement
T = Time

Homework Equations

D=Vf*T - 1/2*a*(t)2

Solve for T

The Attempt at a Solution

I need to solve for T: This is what I got as my attempt but it is so very wrong still
(T)2/T = Vf - 1/2*a -D

Please break down step by step exactly how to do this step by step... I'm seriously struggling here :(

 

[TaxOnFear]

Well, the velocity in the equation is wrong to start with, that's probably why you're struggling.

D = V_iT = 0.5AT²

Rearranging should give you a quadratic.

 

[jtbell]

This is really an algebra question rather than a physics question, so I've moved this to a more appropriate forum.

This is what I got as my attempt but it is so very wrong still
(T)2/T = Vf - 1/2*a -D

Please break down step by step exactly how to do this step by step...

How about instead, you show us step by step how you got to your attempted answer? Then we can show you where you went wrong.

TaxOnFear is correct that you should have a quadratic equation for t. Are you familiar with the "quadratic formula" for solving quadratic equations?

 

[Malelia123]

No I'm not exactly sure what you mean by that.

I just checked the textbook and that is the right equation.

Here is the question I'm stuck on:

If the arresting device on an aircraft
carrier stops a plane in 150 m with
an acceleration of 15 m/s2, find
the time the plane takes to stop.

Here is the equation the textbook says to use:
D=Vf*T - 1/2a(T)2
or
D=1/2(Vf-A*T+Vf)T


This is what I did:

D=Vf*T - 1/2a(T)2
+1/2a

D+1/2a = Vf*T-(T2)
+Vf
D+1/2a+Vf = T-(T)2

and this is where I get stuck... I don't know what to do now?

 

[jtbell]

D=Vf*T - 1/2a(T)2
+1/2a

D+1/2a = Vf*T-(T2)

No, adding (1/2)a to both sides gives

$$D + \frac{1}{2}a = v_f t - \frac{1}{2}at^2 + \frac{1}{2}a$$
$$D + \frac{1}{2}a = v_f t - \frac{1}{2}a (t^2 - 1)$$

 

[Malelia123]

okay - so that is the wrong step? Where do I go from here. I'm sorry I just need a bit more information. I'm missing the basics and a quick reminder will make it click!

If you could even give me a step by step on it, or even a website with some basics too.

 

[jtbell]

As TaxOnFear and I have noted, you really need the quadratic formula to do this. There's no way to rearrange this equation to solve for t "directly." Look up the quadratic formula if you need to refresh your memory.

Then, as a first step, rearrange your equation so it looks like this:

(something)*t² + (something else)*t + (yet something else) = 0

 

[Malelia123]

Would you be able to tell me how you would go about figure out this question:
If the arresting device on an aircraft
carrier stops a plane in 150 m with
an acceleration of 15 m/s2, find
the time the plane takes to stop

Maybe I need to start somewhere? I do not understand the quadric equation business

 

[Mentallic]

Would you be able to tell me how you would go about figure out this question:
If the arresting device on an aircraft
carrier stops a plane in 150 m with
an acceleration of 15 m/s2, find
the time the plane takes to stop

Maybe I need to start somewhere? I do not understand the quadric equation business

I had a hunch you probably wouldn't need to use the quadratic formula in your specific question. You should've given us this question in your first post :tongue:

Think about what v_f is in this question.

 

[Malelia123]

Vf = 0 m/s becuase the plane is stopped.

Should I be finding out what Vi is before find out the time? Ahhh you seem like you know what I need to do... A little hint here

 

[Ray Vickson]

Vf = 0 m/s becuase the plane is stopped.

Should I be finding out what Vi is before find out the time? Ahhh you seem like you know what I need to do... A little hint here

Hint: what is meant by the word "acceleration"? (Yes, I'm serious.) You need to work these things through for yourself; there will be no outside help available on the final exam.

RGV

 

[Malelia123]

Okay people I think I got it:

T=√2*d/A

I've worked through the problem a couple time so I think I have got this.

When Vf or Vi = 0 you use the Scalar form of the equation.

Am I right here?

PS. Seriously thank you, you will probably see me back here. I'm taking Physics 30 & Math 30 applied next semester YIKES.

 

[Mentallic]

Vf = 0 m/s becuase the plane is stopped.

Should I be finding out what Vi is before find out the time? Ahhh you seem like you know what I need to do... A little hint here

Well, think about it. They don't tell us how fast the plane is traveling initially, but they do tell us that it decelerates to a complete stop in 150m at a rate of 15 m/s². Doesn't it seem as though we have enough information to find out what the initial velocity of the plane is? Or even the time it was decelerating for as the question asked.

Using $$D=v_ft-\frac{1}{2}at^2$$

and plugging in $v_f=0$, solving for t isn't quite what you had there. Try again and take it slowly, if you're still not sure, show us each step you take and we'll point at your error.