Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Total distance = 36500 m
The average velocity = 19.73 m/s
Further explanation
Given
vo=initial velocity=0(from rest)
a=acceleration= 1 m/s²
t₁ = 20 s
t₂ = 0.5 hr = 1800 s
t₃= 30 s
Required
Total distance
Solution
State 1 : acceleration
[tex]\tt d=vo.t+\dfrac{1}{2}at^2\\\\d=\dfrac{1}{2}\times 1\times 20^2\rightarrow vo=0\\\\d=200~m[/tex]
[tex]\tt vt=vo+at\\\\vt=at\rightarrow vo=0\\\\vt=1\times 20\\\\vt=20~m/s[/tex]
State 2 : constant speed
[tex]\tt d=v\times t\\\\d=20\times 1800\\\\d=36000~m[/tex]
State 3 : deceleration
[tex]\tt vt=vo+at\rightarrow vt=0(stop)\\\\vo=-at\\\\20=-a.30~s\\\\a=-\dfrac{2}{3}m/s^2(negative=deceleration)[/tex]
[tex]\tt d=vot+\dfrac{1}{2}at^2\\\\d=20.30-\dfrac{1}{2}.\dfrac{2}{3}.30^2\\\\d=300~m[/tex]
Total distance : state 1+ state 2+state 3
[tex]\tt 200 + 36000 + 300=36500~m[/tex]
the average velocity = total distance : total time
[tex]\tt avg~velocity=\dfrac{36500}{20~s+1800~s+30~s}=19.73~m/s[/tex]
The total distance covered by the car will be 36500m and the average velocity of the car for the entire trip will be 19.73 m/sec.
What is average velocity?
The average velocity is the ratio of the total distance traveled to the total time taken by the body. Its unit is m/sec.
The given data in the problem is;
v₀ is the initial velocity=0(from rest)
a is the acceleration= 1 m/s²
t₁ is the time period 1= 20 s
t₂ is the time period 2= 0.5 hr = 1800 s
t₃ is the time period 3= 30 s
For part 1
The distance travelled is found as;
[tex]\rm d=v_0t+\frac{1}{2} at^2 \\\\ \rm d=\frac{1}{2}\times 1 \times (20)^2 \\\\ \rm d=200\ m[/tex]
The initial velocity is found as ;
[tex]\rm v_t=v_0+at\\\\ \rm v_t=0+1 \times 20\\\\ \rm v_t=20 \ m/sec[/tex]
For part 2
The distance traveled is found as;
[tex]\rm d= v \times t \\\\ \rm d= 20 \times 1800 \\\\ \rm d= 36000 \ m[/tex]
For part 3
The acceleration is found as;
[tex]\rm v_t=v_0+at\\\\ \rm 0=v_0+a \times 30\\\\ \rm 20=-30 a \\\\ a= - \frac{2}{3}\ m/sec^2[/tex]
The distance traveled is found as;
[tex]\rm d=v_0t+\frac{1}{2} at^2 \\\\ \rm d=20.30 +\frac{1}{2} \times \frac{2}{3} (30)^2 \\\\ \rm d=300 \ m[/tex]
Total distance travelled= distance travelled( part 1+ part 2+ part3)
Total distance travelled=200+3600+300 = 36500 m
The average velocity is found as;
[tex]v_{avg}= \frac{36500}{20+1800+30} \\\\ v_{avg}= 19.73 \ sec[/tex]
Hence the total distance covered by the car will be 36500m and the average velocity of the car for the entire trip will be 19.73 m/sec.
To learn more about the average velocity refer to the link;
https://brainly.com/question/862972
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
