A. The Tortoise and the Hare A speedy tortoise can run with a speed v_T, and a h

Question

A. The Tortoise and the Hare A speedy tortoise can run with a speed v_T, and a hare can run with a speed v_H. Feeling overly confident, the hare stops for a time delta t_0 to mock the tortoise. The tortoise ends up just barely winning the race by the length of his shell, s. Assume that the animals spend a negligible amount of time accelerating to their top speeds, and that the race ends the moment the winner (the tortoise) crosses the finish line. 1. During the time interval of the race, who runs the greater distance? Explain. If you cannot tell from the given information, state so explicitly. 2. During the time interval of the race, who has the greater average velocity? Explain. If you cannot tell from the given information, state so explicitly. 3. At an instant when they are both running, who has the greater instantaneous velocity? Explain. If you cannot tell from the given information, state so explicitly. 4. Write an expression for the amount of time that the tortoise spent running, delta f_T, in terms of the length of the track, d, and any other variables given in the introduction. 5. Write an expression for the amount of time that the hare spent running, delta f_H, in terms of the length of the track, d, and any other variables given in the introduction.

Explanation / Answer

1)Both the hare and the tortoise runs the same distance.

Since for the race a start and the end point is same for all the contestants and hence the distance is same for both.

2)The tortoise has greater average velocity during the race. Since,

Vav = net displacement/time

He took the less time in finishing the race and hence he got greater avg velocity

3)The Hare has greater instantaneous velocity since the tortoise always covered the given distance with the same velocity

4)speed = distance/time

time = distance/speed

deltaT(t) = d/vt

5)deltaT(h) = d/vh

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