Elementary kinetics problem - Using calculus is different result from algebra

[Femme_physics]

Homework Statement

http://img42.imageshack.us/img42/8172/carxp.jpg

Homework Equations

In my solution

The Attempt at a Solution

My attempt:

http://img208.imageshack.us/img208/6526/xxxxoh.jpg

The actual solution

http://img403.imageshack.us/img403/5579/carsol.jpg

How come they get a different result?

 

[I like Serena]

Hey Fp!

Back to mechanics?

The formulas you're using only apply when acceleration is constant.
See the NOTE at the bottom of the solution.

 

[darkxponent]

v=ds/dt

a=dv/dt=(d^2)s/(dt)^2

are real definitions of acceleration. That is why book has used it. The formula for acceleration you are using comes as special case of this formula. That is special case is when ''acceleration is constant'' and here it is not. So we have to use the 'original' kinematics' equations. Not the kinematics equation used in special case.

 

[Femme_physics]

Hey Fp!

Back to mechanics?

Hi ILS :)
Yep, just trying to stay sharp...am trying to solve kinematics using calculus now which I never really accomplished before :)

The formulas you're using only apply when acceleration is constant.
See the NOTE at the bottom of the solution.

v=ds/dt

a=dv/dt=(d^2)s/(dt)^2

are real definitions of acceleration. That is why book has used it. The formula for acceleration you are using comes as special case of this formula. That is special case is when ''acceleration is constant'' and here it is not. So we have to use the 'original' kinematics' equations. Not the kinematics equation used in special case.

Why is it not defined in the question then whether acceleration is constant or not?

 

[I like Serena]

Hi ILS :)
Yep, just trying to stay sharp...am trying to solve kinematics using calculus now which I never really accomplished before :)

I know. ;)
So is it course material now?

Why is it not defined in the question then whether acceleration is constant or not?

That is implicit from the formula v=3t²+2t.

If the acceleration were constant, you would have a formula like v=2t.
That is, a formula of the form v=v₀+at.

 

[darkxponent]

Why is it not defined in the question then whether acceleration is constant or not?

general equation for acceleration

a=dv/dt

we put a as constant tis gives v=at+c

This means when acceleration is constant v is linearly dependent on 't'. Or we can say that acceleration is constant only when 'v' is linearly dependent on t. In the question it is not. See the question mathematically has given that acceleration is not constant.

"Not everything can be said in words, maths say more''

 

[Femme_physics]

I know. ;)
So is it course material now?

Oh., no, for this current degree I'm done with technical mechanics. Except, I am a teacher now of non-calculus mechanics, so I do have to explain to students kinematics without calculus which is just a matter of formulas of course so I'll get them some practice. I figure if I am doing this then I might as well enrich myself.

Also, to get a first degree in engineering I will have to study more advanced mechanics anyway...so I'm adopting it as a hobby :)

That is implicit from the formula v=3t2+2t.

If the acceleration were constant, you would have a formula for like v=2t.
That is, a formula of the form v=v0+at.

Ahh... makes perfect sense now :) thank you.

 

[OldEngr63]

I notice that you very carefully labeled all your results in m/s, m, etc, when the problem statement was in ft/s, ft, etc. This will get you in trouble. The US Customary system works every bit as well as SI, despite the disparagement it gets from "scientists." If you live in the US, you really need to learn to use it.

 

[I like Serena]

Oh., no, for this current degree I'm done with technical mechanics. Except, I am a teacher now of non-calculus mechanics, so I do have to explain to students kinematics without calculus which is just a matter of formulas of course so I'll get them some practice. I figure if I am doing this then I might as well enrich myself.

Also, to get a first degree in engineering I will have to study more advanced mechanics anyway...so I'm adopting it as a hobby :)

Good!

Are you going for a first degree in engineering then?
Or were you going to anyway and am I misunderstanding what you mean with the current degree?

 

[Femme_physics]

I notice that you very carefully labeled all your results in m/s, m, etc, when the problem statement was in ft/s, ft, etc. This will get you in trouble. The US Customary system works every bit as well as SI, despite the disparagement it gets from "scientists." If you live in the US, you really need to learn to use it.

Oops, force of habit. You're right.

I live in Israel though, we use SI system.

Are you going for a first degree in engineering then?
Or were you going to anyway and am I misunderstanding what you mean with the current degree?

Oh yea, eventually I'll go for a first degree I just got to finish this practical engineer degree first :) I love these stuff.

"Not everything can be said in words, maths say more''

I like that quote :)

So far my favorite quotes

1) Always trust your visual cues - I Like Serena

2) Just remember, Physics is not botany. It's relationships not classification that drive Physics - sophiecentaur

3) "Not everything can be said in words, maths say more" - DarkXponent

 

[I like Serena]

Oh yea, eventually I'll go for a first degree I just got to finish this practical engineer degree first :) I love these stuff.

Wasn't the practical degree enough for your purposes?
Or do you want more now?

I like that quote :)

So far my favorite quotes

1) Always trust your visual cues - I Like Serena

2) Just remember, Physics is not botany. It's relationships not classification that drive Physics - sophiecentaur

3) "Not everything can be said in words, maths say more" - DarkXponent

Ah, you misquoted me, I said "queues", but I like your version better. >_>

 

[Femme_physics]

Ah, you misquoted me, I said "queues", but I like your version better. >_>

:)

Wasn't the practical degree enough for your purposes?
Or do you want more now?

My intellectual pursuit passion conquers me. :) So, no, it's certainly not enough for me!

But we shall see in due time. I just like solving mechanics!

 

[darkxponent]

But we shall see in due time. I just like solving mechanics!

And that 'like' will change into 'love' when you learn calculus.

 

[OldEngr63]

Mechanics without calculus is really pretty tedious, although I must admit that I too fell for it as a student. When I got into calculus, it really took off and began to soar for me. I have been doing it for over 50 years now, and I still enjoy it tremendously. It is definitely more fun that most reading for me.