# A question regarding acceleration

1. Jun 4, 2005

### anthonyy

Hi, I've got a lab requiring me to figure my sustainable and maximum power.

To start with, I'm running distances of 100m, 200m, 300m, and 400m. These runs are then timed, and used to calculate my sustainble power.

So, now, I've got my times (in seconds). Now, I need to find out my sustainable power. To calculate power, I need to use this formula:

-> power = work/time

which is really -> power = force x distance/time

and then, i can turn force into -> power = mass x acceleration x distance/time

ok, so now, i think my formula is ready. (correct me if im wrong)

Now, say my mass is 55kg and the time it took me to run the 100m distance is 14.3 seconds.

I would subsitute these values in, and get this.:

power = 55kg x acceleration x 100m/14.3 seconds

So far, I'm pretty sure that this is also correct, again, correct me if I'm wrong

Now, I need to find out acceleration, it be should it be 9.8/s^2? Because I think it's only used for a falling object, but in this case, I'm running, and not falling. So this is where I'm sorta stuck, is 9.8 the acceleration? or do I have to use an alternative formula to calculate it.

My teacher says that once I have done my graph for all four values (100m, 200m, 300m, 400m), the graph should be a curved line, can anyone confirm this?

Many thanks for the help and advice that will come,

Anthony

Last edited: Jun 4, 2005
2. Jun 5, 2005

### Nylex

The acceleration shouldn't be 9.8 ms^-2 as you're right, that's the acceleration due to gravity and hence is for falling objects. If you knew your speed at a given time, you could use $v = u + at$ or if you knew your speed at a particular distance, you could use $v^2 = u^2 + 2as$ and solve for a in both cases.

3. Jun 5, 2005

### ruby_duby

the only thing i can help you with is the fact that all lines of best fit must be a curved line for science so your teacher is correct

4. Jun 5, 2005

### Nylex

Why is that a fact? What about for plots where one variable varies in direct proportion to the other (so they're meant to yield a straight line)?

5. Jun 5, 2005

### OlderDan

There must be something more going on here than what you have been told, or what you have told us. From the standpoint of basic physics (Newton's Laws), an object in motion will continue in motion in a straight line unless acted upon by an unbalanced force. Running at constant speed requires no net force except to overcome air resistance, so almost no work is done and no power is required. Even on a curved track, where a centripetal force is required to go around the curves, the force is perpendicular to the motion so that force no work. The only work done in your four runs is the work required to accelerate from rest to your constant velocity, plus a small amount to overcome air resistance, for which you have not indicated you have any data.

In reality, the human body expends energy to do simple tasks. For example, to do a series of pull-ups you do no net work because the motion during the up move is in the direction of the force you apply (positive work done by you), but in the down move the motion is opposite the direction of the force you apply, so work is done on you that cancels the work done by you. The same is true of any up and down motion while you are running. To raise your center of gravity, you do some work. When your center of gravity is lowered, work is done on you. No work is done by you to hang from a bar with your arms at a right angle. Yet doing these simple tasks that require no net work wear you out.

There are a couple of things going on here that you need if you are going to find a reasonable answer to your problem, and you cannot find them from just knowing how far you ran in how much time. First, the human body is a complicated force generating machine. Unfortunately, in many cases it is a machine with zero or even negative effieciency. To generate any force requires that energy be expended. To simply hang from the bar, your body must expend energy, but all of that energy is turned into heat while doing no useful work (no motion in the direction of the force). To raise yourself, your body expends far more energy than the useful work it does, converting most of the energy into heat. Even letting yourself back down, while work is being done on you and you are doing negative work epends energy in the form of heat. All of these activities work up a sweat, which is the mechanism whereby your body gets rid of all this excess heat to maintain normal temperature.

The other thing is that while running you are doing real work every time you lift a leg, There is a force applied and a distance moved when you do so. The work done on you by gravity to get that leg back on the ground does you no good. In fact your force generating machine is still running in its inefficient way wasting energy so that you are expending energy to guide you leg down along the proper path to maintain balance during your run.

Maybe you have studied something about bio-physics and have access to information about the energy a body expends to perform ordinary tasks. If so, you need to incorporate that information into your calculation. If you have not, and all you have is distance and time, there is no useful calculation you can do.