Rabbit vs. Tortoise: A 100-m Race

[huong03]

1. A rabbit and a tortoise compete in a 100 meter race. The tortoise moves at a uniform speed of 10 cm/s. The rabbit took a nap for 16 minutes. After the rabbit wake up, he accelerates at a uniform rate of 0.15 m/s^2.
a) Draw a time vs. velocity of the motion of the tortoise and the rabbit? (I'm clueless!)
b) How long does it take for the tortoise to complete the race?
(It takes the tortoise 1000 seconds to win the 100 meter race, right?)
c) How far has the rabbit moved at this time?
d) Who won the race? The tortoise, right? but why?
e) If the rabbit had taken a 15 minutes nap instead, what is his required acceleration for the race to be tie?

2. Is the following formula right?
a) average velocity = (vector)/time

b) average speed = lmagnitudel/ time

Please help, thanks.

 

[Leong]

Use formula
$$s=ut+\frac{1}{2}at^2$$
$$s_{tortoise}=0.10t$$
$$s_{rabbit}=\left\{\begin{array}{cc}0,&\mbox{if}\ t<\ 960\ s\\ \frac{1}{2}*0.15*(t-960)^2, &\mbox{if}\ t\geq\ 960 s\end{array}\right$$
$$v_{tortoise}\frac{ds_{tortoise}}{dt}=0.10$$
$$v_{rabbit}=\frac{ds_{rabbit}}{dt}=0.075*(t-960)^2\ for\ t\ \geq\ 960 s$$
You have got your part (b) correct.
Substitute t=1000 s into the 3rd equation to get 120 m.
Substitute $$s_{rabbit}=100\ m \ to \ find \ the\ time\ t\ taken\ by\ the \ rabbit\\ \ to\ reach\ 100\ m \ to\ get \ t=996.5 \ s.$$
Unfortunately, the rabbit won the race.
Part (d)
$$s_{rabbit}=\left\{\begin{array}{cc}0,&\mbox{if}t<\ 900 s\\ \frac{1}{2}*a*(t-900)^2, & \mbox{if} t\geq\ 900 s\end{array}\right$$
Substitute t=1000 s, time taken by the tortoise to finish the race = time taken for tie to happen, and s=100 m to get the answer.

Convert anything into SI units first. Initial velocity, u, for the rabbit is 0 because it starts from rest.

Can't help you with the next question, not clear enough...

 

[Leong]

Mistake Correction

$$v_{rabbit}=\frac{ds_{rabbit}}{dt}=\frac{1}{2}*0.15*2*(t-960) = 0.15t-144\ for\ t\ \geq\ 960 s$$

The graph is attached.