Respuesta :
Answer:
(a) 2.29 km/h
(b) 9 km/h
Step-by-step explanation:
For part (a) you have to apply the average speed formula, which is defined by:
[tex]v=\frac{d}{t}[/tex]
where d is the total distance traveled and t is the total time needed.
[tex]d=\frac{4.00}{1.75}=2.29[/tex] km/h
For part (b) you have to calculate the running time (T) , which is the total time of the race minus the nap time:
The nap time in hours is:
90/60 = 1.5 h (because there are 60 minutes in one hour)
The running time is:
T= 1.75 - 1.5 = 0.25 h
Let t1 represent the time before the nap and t2 the time after the nap:
t1+t2 = T
t1+t2 = 0.25
You have to apply the formula d=vt before and after the nap:
-Before the nap, the distance traveled was 0.50 km
0.50 = v1t1
-Afer the nap, the distance traveled was 3.50 km
3.50=v2t2
But v2=2v1 (because after the nap the rabbit runs twice as fast)
You have to solve the system of equations:
t1=0.25-t2 (I)
v1t1=0.50 (II)
2v1t2=3.50 (III)
Replacing (I) in (II)
v1(0.25-t2)=0.50
Applying distributive property and solving:
0.25v1-v1t2=.050
For (III) you have that v1t2=3.50/2=1.75. Hence:
0.25v1-1.75=0.50
Solving for v1:
v1 = 9 km/h
The average speed of a rabbit is 2.29 kilometers per hour and his average speed before he stopped for a nap is 9 kilometers per hour.
What is speed?
The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm Speed(v) = \dfrac{Distance (d)}{ Time (t)}[/tex]
A turtle and a rabbit engage in a footrace over a distance of 4.00 km.
The rabbit runs 0.500 km and then stops for a 90.0-min nap.
Upon awakening, he remembers the race and runs twice as fast.
Finishing the course in a total time of 1.75 h, the rabbit wins the race.
(a) The average speed of the rabbit will be given as
[tex]\rm Average \ speed = \dfrac{Total \ distance}{Total \ time}\\\\\\Average \ speed = \dfrac{4}{1.75}\\\\\\Average \ speed = 2.286 \approx 2.29[/tex]
The average speed of the rabbit is 2.29 km per hour.
(b) The average speed before he stopped for a nap will be
Let the average speed of the rabbit before nap and after nap be v and 2v.
Time is taken by the race will be
Time = 1.75 - 1.5 = 0.25 hour.
The average speed will be
[tex]\rm Average \ speed = \dfrac{Total \ distance}{Total \ race \ time}\\\\\\Average \ speed = \dfrac{4}{0.25}\\\\\\Average \ speed = 16[/tex]
Time taken before a nap will be
[tex]\rm t_1 = \dfrac{0.5 }{ v} = \dfrac{1}{2v}[/tex]
Time taken after a nap will be
[tex]\rm t_2 = \dfrac{3.5}{2v}[/tex]
The average speed is given by
[tex]\begin{aligned} \rm Average \ speed &= \rm \dfrac{Total \ distance}{Total \ race \ time}\\\\16 &= \dfrac{0.5 + 3.5}{t_1 + t_2} \\\\16 &= \dfrac{4}{\frac{1}{2v} + \frac{3.5}{2v}}\\\\16 &= \dfrac{4}{\frac{1 + 3.5}{2v}}\\\\16 &= \dfrac{4*2v }{4.5}\\\\72 &= 8v\\\\v &= 9 \end{aligned}[/tex]
More about the speed link is given below.
https://brainly.com/question/7359669
