Struggling with integration

[Joewr13]

Hi I’m stuck on a integration question as I’m not sure how to find v=ds/dt when the S variable isn’t in the original equation I’ve attached a photo it is question a), thanks

 

[Dr.Peterson]

Hi I’m stuck on a integration question as I’m not sure how to find v=ds/dt when the S variable isn’t in the original equation I’ve attached a photo it is question a), thanks

The equation says that ds/dt = 20t + 12t^2.

Integrate, as they say. The goal is to find s, not v.

 

[Joewr13]

The equation says that ds/dt = 20t + 12t^2.

Integrate, as they say. The goal is to find s, not v.

thanks I don’t know how I didn’t see that all I needed was to see the equation wrote in the ds/dt form and i found it pretty easy thanks to you!

 

[Joewr13]

thanks I don’t know how I didn’t see that all I needed was to see the equation wrote in the ds/dt form and i found it pretty easy thanks to you!

I’ve always struggled with integration would u mind taking a look at question B has well I don’t know where to start, would be much appreciated thanks

 

[Dr.Peterson]

I’ve always struggled with integration would u mind taking a look at question B has well I don’t know where to start, would be much appreciated thanks

Again they want you to do nothing but the obvious; but they messed up the wording (as far as the physics is concerned). I don't think it makes any sense at all!

Rather than "the force F required to move an object a distance x meters", they surely mean something like "the force F applied to an object at coordinate x meters". And normally work is calculated as a definite integral, in my experience.

Ignore all that and just do as they say: Replace F with [MATH]4e^{2x}[/MATH] and integrate, choosing the appropriate constant. This is essentially the same as for part (a), just written in terms of an integral (W = ∫F dx) rather than a derivative (dW/dx = F).

 

[Joewr13]

Again they want you to do nothing but the obvious; but they messed up the wording (as far as the physics is concerned). I don't think it makes any sense at all!

Rather than "the force F required to move an object a distance x meters", they surely mean something like "the force F applied to an object at coordinate x meters". And normally work is calculated as a definite integral, in my experience.

Ignore all that and just do as they say: Replace F with [MATH]4e^{2x}[/MATH] and integrate, choosing the appropriate constant. This is essentially the same as for part (a), just written in terms of an integral (W = ∫F dx) rather than a derivative (dW/dx = F).

This helps so much however when calculating a definite integral don’t you need boundary conditions so in this case it would be the distance the object traveled but the question doesn’t state how far the object moved?

 

[Dr.Peterson]

As I said, ignore what they say about the supposed application, and just do what they say, taking an indefinite integral and finding the appropriate constant, as you did in the other part.

That is, pretend all they gave you was this:

 

[Joewr13]

As I said, ignore what they say about the supposed application, and just do what they say, taking an indefinite integral and finding the appropriate constant, as you did in the other part.

That is, pretend all they gave you was this:
View attachment 27791

Ohhh that is so much easier to understand thanks a lot!