A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. The hare accelerates uniformly at a rate of 0.9 m/s2 for 4.5 seconds.

Question

A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. The hare accelerates uniformly at a rate of 0.9 m/s² for 4.5 seconds. It then continues at a constant speed for 13.9 seconds, before getting tired and slowing down with constant acceleration coming to rest 74 meters from where it started. The tortoise accelerates uniformly for the entire distance, finally catching the hare just as the hare comes to a stop.



1) How fast is the hare going 2.7 seconds after it starts?   

2) How fast is the hare going 9.2 seconds after it starts?

3) How far does the hare travel before it begins to slow down?

4) What is the acceleration of the hare once it begins to slow down?

5) What is the total time the hare is moving?

6) What is the acceleration of the tortoise?

Answer 1

To answer these questions, you would need to know the kinematic equations:

d = v_o*t + 0.5*a *t²

v_f = v_o + a*t

v_f² = v_o² + 2 *a *d

d = (v_o + v_f)/ 2* t

where

d = displacement

t = time

a = acceleration

v_o = original or initial velocity

v_f = final velocity

1) For the first part, what are we trying to find here? Velocity? Acceleration? Usually when the question asks "How fast" something is going it usually is the magnitude of the velocity, speed. At 2.7 seconds, the hare is still constantly acceleration. Remember, that the initial velocity is zero because the hare starts from rest.

What is a kinematic equation that uses time and acceleration to get a final velocity?

**If you want to get a clear idea of how the hare and tortoise move, you can graph their velocities in a velocity versus displacement graph.**

2) At 9.2 seconds, the hare is going at a constant velocity. But how do we know the velocity at which the hare is travelling? The velocity is the same as the final velocity the hare has after travelling 4.5 seconds with constant acceleration.

What is a kinematic equation that uses time and acceleration to get a final velocity, considering initial velocity to be zero?

3) The hare travels 4.5 seconds with constant acceleration and then 13.9 seconds with constant velocity(found in part 2) before slowing down.

What are the two equations you should use to find the distance travelled?

**HINT: You should use one equation for constant acceleration and another equation for the constant velocity distances. After you find these two distances add them together.**

4) The information from the passage states that the initial velocity is the same velocity from part 2 and the final velocity is zero,

What equation can be used to find the acceleration given the final velocity, initial velocity, and distance travelled?

5) You are given the time for all parts except for the period where the hare slows down. Because we found the acceleration in part 4, we can use that to find this time.

What equation would you use to find time, given the acceleration (negative because it is slowing down), initial and final velocities?

To find the total time add the times given in the passage with the time found in this part.

6) The passage states that the tortoise meets the hare when the hare stops. This means that distance traveled and the time should be the same for the tortoise and the hare at this point. We have already found the total time in part 5 . The total distance travelled can be determined from part 3, and the information given in the passage.

What equation would you use to find acceleration given the time, the distance, and the initial velocity (tortoise starts from rest)?

Hope this helps!