Graphing of Displacement and Velocity
The final race is to be hopped over 20 m, now let’s Make our value to be 22 m since a race must have a definite value to define the distance. Therefore, the finishing line will be at 22 m. The cane toad race is sport where toads compete (Hung, 2008) (Fountain, 2007). The table below represent the distance covered by the toads within the indicated time.
Drawing the graph of the toad velocities
Velocity equation is obtained by getting the derivative of the displacement equation (Anderson, et al., 1994) (Jones, 2010). Therefore for;
Calculation of the velocity of each toad after
1 minuteWhen the one toad fist overtakes the other After 0.8 minutes where Flash overtake Gonsales.Toad velocity at 0.8 minutes
Gonsales; 0.0381m/mn
Flash: -5.44m/mn
Road Runner: 0.0056m/mn
The fastest speed is
22.07m/mn which is reached by Flash at the time it cuts the finishing line at 22 m point
The greatest rate of change of speed
The rate of change of speed is termed as acceleration (a)
This value is obtained by differentiating the equation of the speed.
acceleration is obtained by the toad Gonsales at the time it reaches the finishing line. This is 1.993 The first placed toad is Flash while the second placed toad is Gonsales. This can be seen from the displacement graph in figure 1
The distance between them can be obtained by subtracting their displacements at each of the given points. Now looking at table 1; when the toads are at 13.8 minutes. Gonsales it at 6.2803m while Flash is at 1.5426m the distance between then is 4.7377 m. this is the greatest distance between the two toads.
Modelling and Problem solving
- Yes, at time 0 minutes before the race began Gonsales is already at 0.1 m. this means the toad started with a handicap.
- No, when you study the displacement graph of the three toads you realize the following; Gonsales is always travelling towards the requires direction. Flash alternates. From 0 to 4 minutes it moves in the right direction then from 4 to 12 minutes it changes direction and moves in the wrong one. After the 12thminute till it reaches the finishing line it moves in the right direction. In the case of Road Runner from the start to 16 minutes it moves in the right direction after which it changes and start moving towards the wrong direction.
- The toad which wins the race is Flash. It takes 1044 seconds to complete the race. Gonsales comes second with 1060 seconds. This means Flash won by 16 seconds
The equation for the behaviour of Hop-a-long will be The displacement graphs
The outcome of the race has not changed. Hop-a-long have finished third behind Flash and Gonsales. There is no proof that Road Runner managed to finish the race as it keeps on going towards the wrong direction.
The assumption made is that the finishing line will be at the 22m mark.
Radio call commentary
Hallow listeners? It’s just a few minutes before the sport cane toad racing kicks off. Let’s have a review of the competitors. There will be four toads taking part on today’s final; Gonsales, Flash, Road Runner and Hop-a-long. Initially we thought Hop-a- long was injured and won’t take part, to our surprise the toad seems to have made a miraculous recovery and is on the line up.
There we go, the race starts and Gonsales have started with a handicap the toad is already 0.1m and have taken an early lead.
We are at the 48th seconds in to the race and Flash have just overtaken Gonsales. The race is a bit tight as the two toads appear to be very close.
Flash continuous to lead the race ahead of Gonsales but Road Runner is making a very strong chase.
It’s the 202th second since the race kicked off and Road runner have just overtaken Flash who seems to have grown tired. Road runner continues to lead and is now being chased by Flash, Gonsales with Hop-a-long coming a distance fourth. The toad seems to have not made a full recovery it has been at the bottom from the 12 second to now.
Determining the Fastest and Slowest Toads
Flash is having difficulties focusing on the right direction and Road Runner have taken the opportunity to steal the race, the toad seems to be at the verge of taking the gold medal. At the 564th second and Gonsales have now overtaken flash to chase the silver. Road Runner still maintains the lead.
Just at the 624th second and now even Hop-a-long have managed to overtake flash, with flash continuing to move towards the wrong direction seems like Hop-a-long may just get a medal after all. Road runner is still maintaining the lead.
Hop-a-long does not get to enjoy being in front of Flash for a long time just at the 672th second and it goes back to its bottom position. Hop-a-Long again overtakes flash at the 69th second this two seems to be really making a competition for the third position. Road Runner is just on the verge of completing the race with just around 5.2 m remaining at the 696th second.
Just at the 948th second when Road Runner was just about to grab the gold the toad instantly changes its direction. This is miraculous, flash have now focused on the right direction and is quickly gaining momentum. It has already overtaken Hop-A-Long and is giving Gonsales a chase.
At the 996th second and flash is now number two. Road Runner continuous to fumble near the finishing line.
Flash just increased its speed and at the 1044th second finishes the race Gonsales is now closing in on Road runner for the Silver medal
At the brink of 1060th second Gonsales secures the silver with hop-a-long continuing to chase the bronze at the expense of really confused Road Runner.
In the 1193rd second and Hop-a-long secures the bronze the confused Road Runner still maintains the wrong direction. It appears the toad is just going back to the starting point.
And there we have it Flash secures the gold, Gonsales silver with Hop-a-long managing to secure bronze despite just recovering from an injury.
Commentary script
Analysis of the toads’ race
Gonsales has a velocity given by , Flash and Road Runner ). The road runner’s major strength is that it can move very fast in the right direction for a short distance. The toad is very effective for winning races of less than 20m
On the other hand, Gonsales is reliable, the toad never changes focus as far as direction is concerned. Its only limitation is the slow speed.
When we come to flash, the toad possesses hidden abilities in the short run it tends to be confused but once focused its speed increases tremendously. This is the right toad to back for long races.
Hope along though have no issue with maintaining its velocity towards the same direction the toad is extremely slow and can only get a win in a case where others are confused in terms of following the right direction.
Assumptions
The race was for a 22m length
A winner toad gets Gold, second places silver and third placed Bronze. There is no present out of these positions.
Justification for the race.
Cane toad racing provided people with a chance to get entertained while at the same time giving room for gamblers to make some cash (Sullivan, 1979).
References
Anderson, D., Sweeney, D. & Williams, T., 1994. Introduction to Statistics: Concepts and Applications, s.l.: West Group.
Fountain, H., 2007. Arthritis Fails to Slow Invading Toads in Australian Fields, NY: NY Times.
Hung, L., 2008. Hung cane toad racing in Darwin-narated by Russell Crowe.wmv. [Online]
Available at: https://www.youtube.com/watch?v=ezME0Onkatg
[Accessed 13 May 2018].
Jones, S., 2010. Statistics in Psychology: Explanations without Equations, s.l.: Palgrave Macmillan.
Sullivan, G., 1979. The Complete Sports Dictionary, New York: Scholastic Book Services.
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