How can I solve this integrals problem?

[lasvegas666]

'

 

[mario99]

View attachment 37812'

Integrate both sides as before.

 

[lasvegas666]

Integrate both sides as before.

So velocity is a derivative of speed?

I got it now.

 

[mario99]

So velocity is a derivative of speed?

I got it now.

Velocity [imath]v(t)[/imath] is the derivative of position [imath]s(t)[/imath].

 

[The Highlander]

Velocity is not the derivative of "speed" or "position"; it is the derivative of displacement wrt time: \(\displaystyle \frac{\mathrm{ds}}{\mathrm{dt}}\)

 

[mario99]

Velocity is not the derivative of "speed" or "position"; it is the derivative of displacement wrt time: \(\displaystyle \frac{\mathrm{ds}}{\mathrm{dt}}\)

You said velocity is the derivative of displacement[imath]\displaystyle \frac{d}{dt}(s - s_0)[/imath], yet, you wrote position [imath]\displaystyle \frac{d}{dt}(s)[/imath].

 

[The Highlander]

You said velocity is the derivative of displacement[imath]\displaystyle \frac{d}{dt}(s - s_0)[/imath], yet, you wrote position [imath]\displaystyle \frac{d}{dt}(s)[/imath].

Displacement (s) is a vector quantity (with magnitude & direction), it is not (s - s₀).

It's magnitude might be determined by (p - p₀), where p & p₀ are two positions (current & initial respectively) and so it should be written as:-

\(\displaystyle \frac{\mathrm{ds}}{\mathrm{dt}}\) or \(\displaystyle \frac{\mathrm{d}}{\mathrm{dt}}\mathrm{s}\)​

 

[mario99]

Displacement (s) is a vector quantity (with magnitude & direction), it is not (s - s₀).

It's magnitude might be determined by (p - p₀), where p & p₀ are two positions (current & initial respectively) and so it should be written as:-

\(\displaystyle \frac{\mathrm{ds}}{\mathrm{dt}}\) or \(\displaystyle \frac{\mathrm{d}}{\mathrm{dt}}\mathrm{s}\)​

You meant to say [imath]\bold{v} = \displaystyle \frac{d}{dt}\bold{s} = \displaystyle \frac{d}{dt}(\bold{p} - \bold{p_0})[/imath]

But

[imath]\bold{v} = \displaystyle \frac{d}{dt}(\bold{p} - 0) = \displaystyle \frac{d}{dt}(\bold{p})[/imath]

Which is still the derivative of position.

 

[The Highlander]

You meant to say [imath]\bold{v} = \displaystyle \frac{d}{dt}\bold{s} = \displaystyle \frac{d}{dt}(\bold{p} - \bold{p_0})[/imath]

But

[imath]\bold{v} = \displaystyle \frac{d}{dt}(\bold{p} - 0) = \displaystyle \frac{d}{dt}(\bold{p})[/imath]

Which is still the derivative of position.

No, it is the derivative of displacement.
Please don't engage in any further semantic argument; this is an already well defined concept.

 

[khansaheb]

You have been asked to find the position function - given the speed function

 

[mario99]

No, it is the derivative of displacement.
Please don't engage in any further semantic argument; this is an already well defined concept.

I have just shown you that it is not wrong to say velocity is the derivative of position in this problem of #1. It is up to you how far you wanna go with your argument.

I am done.