Respuesta :
Answer:
Average velocity is 32 miles/hr.
Step-by-step explanation:
Given that a particle moves on a line away from its initial position so that after t hours it is [tex]s=6t^2+2t[/tex] miles from its initial position.
We have to find the average velocity of the particle over the interval [1, 4].
As, average velocity is the change is position over the change in time.
[tex]s(4)=6(4)^2+2(4)=104[/tex]
[tex]s(1)=6(1)^2+2(1)=8[/tex]
∴ [tex]\text{Average Velocity=}\frac{s(4)-s(1)}{4-1}[/tex]
=[tex]\frac{104-8}{3}=\frac{96}{3}=32miles/hr[/tex]
Hence, average velocity is 32 miles/hr.
The average velocity of the particle is [tex]\boxed{{\mathbf{21 units}}}[/tex] .
Further explanation:
Velocity is the speed of an object in a given direction. Velocity is the vector quantity.
The average velocity can be calculated as,
[tex]{\text{average velocity}}=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}[/tex]
Given:
The position of the particle after [tex]t[/tex] hours is [tex]s\left(t\right)=4{t^2}+t[/tex] . The given interval is [tex]\left[{1,4}\right][/tex] .
Step by step explanation:
Step 1:
The position of the particle after [tex]t[/tex] hours is [tex]s\left(t\right)=4{t^2}+t[/tex]
First we need to find the distance travelled in the interval of [tex]\left[{1,4}\right][/tex] .
The distance travelled by the particle at [tex]t=1[/tex] is as follows,
[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(1\right)=4{\left(1\right)^2}+1\hfill\\s\left( 1 \right)=5\hfill\\\end{gathered}[/tex]
The distance travelled by the particle at [tex]t=4[/tex] is as follows,
[tex]\begin{gathered}s\left(t\right)=4{\left(t\right)^2}+t\hfill\\s\left(4\right)=4{\left(4\right)^2}+1\hfill\\s\left( 1 \right)=68\hfill\\\end{gathered}[/tex]
Now find the distance travelled by the particle in the interval of [tex]\left[{1,4}\right][/tex] .
[tex]\begin{aligned}{\text{distance travelled}}&=s\left(4\right)-s\left(1\right)\\&=68-5\\&=63\\\end{aligned}[/tex]
Step 2:
The given interval is [tex]\left[{1,4}\right][/tex] .
Now we need to find the time as,
[tex]\begin{aligned}{\text{time elapsed}}&=4-1\\&=3\\\end{aligned}[/tex]
Step 3:
Now we find the average velocity of the particle.
The average velocity can be calculated as,
[tex]\begin{aligned}{\text{average velocity}}&=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}\\&=\frac{{63}}{3}\\&=21{\text{units}}\\\end{aligned}[/tex]
Therefore, the average velocity of the particle is [tex]21{\text{ units}}[/tex] .
Learn more:
- Learn more about the distance between the points https://brainly.com/question/6278187
- Learn more about Adam drove his car 132 km and used 11 liters of fuel. How many kilometers will he cover with 14 liters of fuel? https://brainly.com/question/11801752
- Learn more about the equivalent fraction https://brainly.com/question/952259
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Speed, distance and time
Keywords: velocity, initial position, particle, moves, interval, distance travelled, time elapsed, position, average velocity, units, vector quantity, speed, direction, hours.
