Physics: Motion in One Dimension: The Tortoise and the Hare Race; Kinematics

[TheDragon]

A turtle and a rabbit engage in a footrace over a distance of 4.00km. The rabbit runs 0.500km and then stops for a 90min nap. Upon awakening, he remembers the race and runs twice as fast. Finishing the course in a total time of 1.75h, the rabbit wins the race.

A) Calculate the average speed of the Rabbit.

~I knew how to find the avg speed by dividing 4.00km and 1.75h. i got 2.28km/h

B) What was his average speed before he stopped for a nap? Assume no detours or doubling back.

~I converted the break of 90min to 1.5h.  and i know that more than one step is required to answer this. I just don't know where to start.

The question is asking to find the answers in km/h

 

 

[studiot]

There's too much information here, but let's see

 

The rabbit runs 0.5km at v and the remaining 3.5km at 2v.

According to your information this takes (1.75 - 1.5) = 0.25 hours

Can you write an equation in v connecting these facts?

[TheDragon]

I have no clue. It's making me frustrated. I know that the times for both trips minus the break arent known. and the rabbit goes twice as fast the first avg speed.

[studiot]

OK so what what equation connects distance, speed and time?

That's easy isn't it?

[TheDragon]

v=d/t.

[studiot]

so t = ?

This is just in general, not specific to this problem.

Edited September 3, 2018 by studiot

[TheDragon]

t=d/v. 

[studiot]

Yea.

So on the first 0.5km if his speed is v what is t₁ ?

You only have one number to put in that equation you just wrote

t₁ = ?

Edited September 3, 2018 by studiot

[TheDragon]

My brain is honesty fried right now. Im too frustrated to even think clearly.

[studiot]

How do you feel about

t₁ = 0.5/v  ?

?

Well you have obviously gone to bed for your well earned rest.

If it all becomes clear in the morning perhaps you can find a similar expression for t2 in terms of the distance run and v, the original velocity?

then you know the total of t₁ and t₂ so if you can then form an equation by adding them together and equating their sum to this, you can solve it for v , which is the speed you require.

 

I would be interested if you would post your quation and how you solved it

Then I will show you my version, which may be of interest.

 

Good night anyway.

[studiot]

Inreference to your pm well done for solving it. +1

I have replied there about the posting restriction.

Quote

for some reason it isnt letting me post anymore. But i did solve it.  t=d/t

 

0.25h= 0.500km/v1+ 3.50/2v1 

0.25h= (2)0.500km/(2)v1 + 3.50/2v1

0.25h= 1km/2v1 + 3.50/2v1

0.25h= 4.50km/2v1

0.25h(2v1)= 4.50km

2v1= 4.50km/(0.25h)

2v1= 18km/k

v1=18km/h/2

v1=9km/h

I solved the equation like this - I used just v instead of v1 for the velocity

[math]\frac{{0.5}}{v} + \frac{{3.5}}{{2v}} = 0.25[/math]

The first thing to do is to clear the fractions so multiply though by v

[math]0.5 + \frac{{3.5}}{2} = 0.25v[/math]

Then multiply through by 4

[math]2 + 7 = v[/math]

 

I hope you will see that this is easier.

 

[Sensei]

On 3.09.2018 at 11:07 PM, TheDragon said:

I just don't know where to start.

I would start from drawing entire race on timeline (graph) to visualize it.. x-axis could be time, and y-axis distance.

Edited September 5, 2018 by Sensei