Calculating Acceleration: A Sprinter's Challenge

[PabloPicasso]

Hey guys, my professor assigned an extra credit problem worth a good 100 points, I would appreciate if someone can demonstrate me this problem.

Two sprinters compete. Each accelerates at a uniform rate from a standing start. Al covers the last ¼ of the distance in 3 seconds; Bob covers the last 1/3 in 4 seconds. Who won and by how much ( the the nearest 0.001 second)?

 

[whozum]

Spit out some thoughts, have you done any physics in your time?

 

[PabloPicasso]

yeah but i forgot how to do these types, can u please help me?

 

[James R]

Show us what you've done so far.

 

[PabloPicasso]

v=d/t

1/4=3x
x=1/12

1/3=4y
y=1/12

 

[whozum]

That v stands for average velocity. You want an expression for constant acceleration.

 

[PabloPicasso]

can u please set up the problem for me with an appropriate equation?

 

[MJCfromCT]

Think of how velocity relates to acceleration.

 

[The Guru Kid]

It might help if you looked at it in terms of differentials. Like v= dx/dt instead of x/t.

 

[PabloPicasso]

will someone please show me at least the starting equation + work so that I may take it from there?

 

[whozum]

Does this look familiar

$$x-x_0 = v_0t + \frac{1}{2} at^2$$

 

[PabloPicasso]

wow thanks guys, that really helped...now my professor assigned a second extra credit, how would i begin doing this one?

Cylindrical soup cans are to be manufactured to contain a given volume V. There is no waste in cutting metal for the sides of the can, but the circular endpieces will be cut from a square, with the corners wasted. Find the ratio of height to radius for the most economical can.

 

[whozum]

I think you're misunderstanding hte point of this forum. We aren't here to do your homework. We're here to help you if you're struggling with an idea.

Show me why/where I should help you.

 

[PabloPicasso]

i just need help in what formula to use for that 2nd question i gave, ill do the rest

 

[whozum]

i just need help in what formula to use for that 2nd question i gave, ill do the rest

There is no 'formula' one can just plug things into and everything will be handy dandy. Part of these word problems is to be able to figure out a formula to use that fits the problem and will help yo usolve it. If I told you the formula to use, I would be doing the hard part for you, which isn't the point.

You come up with it yourself, I'll help you if you need, but tell me what you think you need to do.

 

[PabloPicasso]

i would learn much easier if i was given a formula by ANY of u...GEEZ for Christs sake how many times do i have to post to get a formula out of this forum? I am not asking you guys to do it for me for cryin out loud, if i can just get an appropriate formula for this problem, i can do the rest on my own, now can someone help?

 

[James R]

PabloPicasso:

If you have a can with radius r and height h, what would be the volume of the can? And what area A of material will it require to manufacture it? Give formulas for V and A in terms of r and h.

Now, what does "most economical" mean, in the problem statement?

How can you find the most economical can using your formulas?

Have a go at this, and post your working.

 

[Jameson]

This problem does not have a standard formula. Most of the max/min problems in Calculus have parts of different formulas. Actually writing the expression for the volume here is the hardest part. Once that is done, all you need to do is differentiate.

The basic form for the volume of a cylinder is :

V = area of base * height