Please help: Derivative - Question

[sam_calculus]

Can somebody please tell me how to approach a problem like this:
"A thief 40 meters away runs towards you at 8 meters per second. What is the smallest acceleration so that v = at keeps you in front?"

Thanks a lot in advance!

 

[Deleted member 4993]

Can somebody please tell me how to approach a problem like this:
"A thief 40 meters away runs towards you at 8 meters per second. What is the smallest acceleration so that v = at keeps you in front?"

Thanks a lot in advance!

Please follow the rules of posting in this forum - enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts with us - so that we know where to begin to help you. Also include the context - is it a problem from calculus class (you posted in calculus forum), or from physics class, or from "engineering dynamics" class - or something else.

Please post the EXACT problem as it was presented to you. Your post - as displayed, does not make sense.

 

[Dr.Peterson]

Can somebody please tell me how to approach a problem like this:
"A thief 40 meters away runs towards you at 8 meters per second. What is the smallest acceleration so that v = at keeps you in front?"

I suppose that the acceleration means your own acceleration from 0 (not the thief's), and "keeps you in front" means "prevents him from catching you".

I can think of several ways to do this, some not using calculus apart from expressing your position as a function of time.

If you graph the position of each person, you want the parabola not to intersect the line. Find that any way you want. But as I read it, there is no answer, technically, because there will be an acceleration at which the curve and line will just touch, and anything above that will keep you safe (depending on how long his arms are). There is no minimum!

Please do as SK asked, so we can provide the specific help you need.

 

[sam_calculus]

Please follow the rules of posting in this forum - enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/

Please share your work/thoughts with us - so that we know where to begin to help you. Also include the context - is it a problem from calculus class (you posted in calculus forum), or from physics class, or from "engineering dynamics" class - or something else.

Please post the EXACT problem as it was presented to you. Your post - as displayed, does not make sense.

Thanks. I will revert with my work and reply.

 

[sam_calculus]

I suppose that the acceleration means your own acceleration from 0 (not the thief's), and "keeps you in front" means "prevents him from catching you".

I can think of several ways to do this, some not using calculus apart from expressing your position as a function of time.

If you graph the position of each person, you want the parabola not to intersect the line. Find that any way you want. But as I read it, there is no answer, technically, because there will be an acceleration at which the curve and line will just touch, and anything above that will keep you safe (depending on how long his arms are). There is no minimum!

Please do as SK asked, so we can provide the specific help you need.

Thanks. Will do.