How Do I Solve This Spring Differentiation Problem in Physics?

[cracktheegg]

Homework Statement

Differentiation question on physics spring

https://sg.answers.yahoo.com/question/index?qid=20140819111550AAvmAjH

Homework Equations

The Attempt at a Solution

https://www.icloud.com/photostream/#AEGY8gBYGdYO6S;2B1E78BF-9378-47B0-B87C-BD50541B4EE7

Why I can't get the answer given: am I wrong or the answer given wrong

Can anyoneelse work it out and see the answer

 

[BvU]

To put it bluntly: you are wrong.

Don't really appreciate your way of using the template, but never mind. I hope I don't get thrown out of PF for helping anyway. The hint is: integrating $dx\over x^2+7^2$ does not yield a ln. (Check by differentiating !)

 

[Simon Bridge]

For the sake of anyone else checking in: the problem statement is:

C1. a mini-van of mass 1200kg is traveling along a level road. The resistance to the motion is (v^2+49)N where v (m/s) is the instantaneous velocity at any time t (s). When the velocity of the mini-van reaches 16m/s, the engine is shut off.

(a) write the DE of motion connecting v and t
(b) find the time taken for the velocity to reduce from 16m/s to 12m/s
(c) ...

You are asking about C1.b.

How do I solve this differential question,I can do c1 part [a] but how to do b)? Why am my previous working wrong? please help?

You have written $$1200\frac{dv}{dt} = -(v^2+49) \\ \implies t=-\int \frac{1200}{v^2+49}\;dv$$ ... you actually wrote t+c=... but the arbitrary constant gets absorbed into the integral on the RHS.

You show no working for the integration - as BvU suggests, this is where you need to look closer.
You appear to have got: $$\int\frac{dv}{v^2+49}=\ln(-v+7)+\ln(v+7)$$... which would be incorrect.
It is unclear how you did that.

As a matter of routine, you should check your solution to DEs by substituting them back.
Do try to write out your questions in PF, it makes it easier to help you.

 

[HallsofIvy]

-(v^2- 49) factors as (-v+ 7)(v+ 7) but -(v^2+ 49) does not.

 

[Simon Bridge]

Maybe OP read $-(v^2+49)$ as $-v^2+49$ ?

 

[BvU]

Is eggcracker still in the picture ? What of the integral of $1\over x^2+a^2$ ?

 

[Simon Bridge]

'S only been a day ... @eggcracker: any of this helpful so far?
More assistance with feedback.