# How Can a Slower Runner Catch a Faster One?

Acceleration is the key for a predator chasing down swifter prey

Kinematics, the study of motion and how things move, encompasses the concepts of position, velocity and acceleration—but as anyone who has caught up to someone in a game of tag or on the running track knows, it's acceleration that's the most fun element of this concept.

Some of us start out slow, but acceleration can yield some surprising results when it comes to predators and prey, or basically anyone involved in a chase. As the kinematics episode of NBC Learn's "The Science of NFL Football" states, "NFL running backs would be easy prey, and football itself wouldn't be nearly as fun to watch" without acceleration and other aspects of kinematics.

Football players, track runners, prey eluding predators—all basically want to reach their top velocities, or accelerate, as quickly as possible.

So here's a brain puzzle to help you work through this issue. Take a look at the graph below, which shows the velocities of a gazelle (the prey) and a lion (the predator) over time. Velocity in meters per second is on the y axis (vertical) and time in seconds is on the x axis (horizontal).

Which of the following is true for a lion attempting to catch a gazelle?
A. The lion should chase the gazelle for as long as possible to maximize the chance of catching it.
B. The lion should chase the gazelle until the gazelle reaches its maximum velocity.
C. The lion should give up the chase if he hasn't caught the gazelle within four seconds.
D. The gazelle doesn't have to worry about lions, because it can run about twice as fast.
E. The gazelle travels farther than the lion does in the first two seconds of the chase.

Now imagine that the lion is a linebacker and the gazelle is a fleet-footed running back. In the 40-yard dash, the running back always beats the slower linebacker. But in real games, the linebacker has a chance to make the tackle if he can accelerate faster than the running back—yet if he doesn't catch him in the first four seconds, he may as well forget it. (The correct answer is C.)

Of course the situation works the other way, too—a slower running back could elude a swifter defensive back if he can accelerate fast enough, perhaps reaching the end zone before the defender can catch him. As former New Orleans Saints running back "Deuce" McAllister explains in the video, "You're going to beat him to his top speed, therefore you're going to be more successful than he is." Acceleration can make you a winner, even if your opponent can ultimately run faster than you.

The graph is courtesy of J.A. Bolker and D.C. Meredith, University of New Hampshire, and is based on data from Elliott, P.; Cowan, I. M.; and Holling, C. S., 1977. Prey capture by the African lion. Canadian Journal of Zoology 55(11):1811-1828.

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1. 1. DaoudaW 03:50 PM 11/12/10

About 20 years ago I observed this scenario with a twist. The lion approached the herd of gazelles slowly while hidden by a large termite mound. I expected her to stop when she reached the mound, but she smoothly stepped around the mound while watching expectantly. To my great disappointment, she didn't chase. After reading the article I'm sure she realized that she wouldn't have had a chance to catch a gazelle in those first few seconds; they were too far away.

2. 2. reflectogenesis 02:33 AM 11/13/10

What about the effects of scale and inertia and air and wind rsistance. Supposing a stick insect was trying to escape a gecko?

3. 3. reflectogenesis 02:35 AM 11/13/10

A human escaping an elephant in a strong wind?
Would the human first have to read Scientific American?

4. 4. reflectogenesis 02:41 AM 11/13/10

And what about reactions and brain state.
A tiger wouldn't have to run at all if it was down wind and camouflaged.
Would one gazelle on its own necesssarily see a tiger, even in the open, unless it pointed its head in the right direction

5. 5. reflectogenesis 07:41 AM 11/13/10

I don't really understand this at all.
If the slower runner sees that the faster runner is running - then to reach him he must first get to the halfway point between himself and the faster runner. When he reaches this point he must again reassess how far he has to go to reach the faster runner. Again he must get to the halfway point between himself and the faster runner before he can assess the situation. At this point he will see that to reach the faster runner he must again first get to the halfway point between himself and the faster runner before he can again reassess his position. When he reaches this point he sees that he must again first get to the halfway point between himaself and the faster runner before he can again assess his situation whereupon he will find that to reach the faster runner he must again first reach the halfway point between himself and the faster runner.
I suggest that it might pay him to stop running and assess this sequence of events before continuing to try and catch the faster runner.
I think he will upon inspection conclude that he is never going to catch the faster runner but rather is only ever going to get half way toward him. Thus the faster runner is undoubtedly - in an even race - always going to outstrip the slower runner.
This is just the common sense conclusion that the faster runner can run faster than the slower runner and so can never be caught.

6. 6. reflectogenesis 07:51 AM 11/13/10

Is it necessary therefore that the lion needs, not outright acceleration to catch the gazelle but rather requires a change of acceleration to catch the gazelle?
So its all in that last pounce which might result from a transfer of rotational kinetic energy into linear acceleration so that the claw can reach its target?
reflectogenesis@hotmail.co.uk

7. 7. reflectogenesis 07:53 AM 11/13/10

And is this not more often than not how the wide receiver gets the touch down?

8. 8. Hiriver in reply to reflectogenesis 10:38 AM 11/13/10

well,what you say is fun,digg!

9. 9. Ralf123 12:43 PM 11/13/10

Hmm. 9th grade matter in SciAm? I'm not impressed.

10. 10. williweb 07:45 AM 11/14/10

A very interesting twist on the chase parameters is the cheetah, which is faster than the gazelle, but only for a few seconds. A domestic house cat will show you the competitive edge of stealth while approaching a bird. It knows how close it must get to even attempt the chase, weighing the distance and stealth factors up to the last second.

11. 11. bucketofsquid 06:01 PM 11/17/10

refletcogenesis - How long have you been schizophrenic? That is the most poorly thought out and disorganized set of rambling posts I've seen in a long time. Tigers and gazelles are not native to the same continents. The article discusses linear chases and the fact that rapid acceleration is more significant at the start of a chase but top speed is more significant as the chase continues. Stealth is not relevent to the topic of the article.

12. 12. reflectogenesis 06:32 PM 11/17/10

Another sciam article describes the interchange between information and energy. On these grounds the acceleration of an organism must start in its head.
F=ma KE =1/2 mv(2) E=mc(2)
The answer is somewhere in there.
I can see you accelerating toward your keyboard now.
But the process has started at this end of the Atlantic.

13. 13. reflectogenesis 06:45 PM 11/17/10

And anyway - supposing we are all schizophrenic - and because we are all so - then why should we notice it?
Julian Jaynes argued that all humans were schizophrenic before 3000 years ago - doing what the Gods literally told them to do via voices in their head. He showed good evidence of this in the literature of the time.(Homer etc)
But I don't think he really considered the possibility that we are all schizophrenic now - and those people prior to 3000 years ago were infact normal and that if we listened hard enough - then the Gods would tell us what to do.

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