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guapka [62]
3 years ago
9

@bobross plz help I have another question

Mathematics
2 answers:
vampirchik [111]3 years ago
8 0

The average velocity of the particle is \boxed{{\mathbf{21 units}}} .

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,

{\text{average velocity}}=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}

Given:

The position of the particle after t  hours is s\left(t\right)=4{t^2}+t . The given interval is \left[{1,4}\right] .

Step by step explanation:

Step 1:  

The position of the particle after t  hours is s\left(t\right)=4{t^2}+t  

First we need to find the distance travelled in the interval of \left[{1,4}\right] .

The distance travelled by the particle at t=1  is as follows,

\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}

The distance travelled by the particle at t=4  is as follows,

\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}

Now find the distance travelled by the particle in the interval of \left[{1,4}\right]  .

\begin{aligned}{\text{distance travelled}}&=s\left(4\right)-s\left(1\right)\\&=68-5\\&=63\\\end{aligned}

Step 2:  

The given interval is \left[{1,4}\right] .

Now we need to find the time as,

\begin{aligned}{\text{time elapsed}}&=4-1\\&=3\\\end{aligned}

Step 3:  

Now we find the average velocity of the particle.

The average velocity can be calculated as,

\begin{aligned}{\text{average velocity}}&=\frac{{{\text{distance travelled}}}}{{{\text{time taken}}}}\\&=\frac{{63}}{3}\\&=21{\text{units}}\\\end{aligned}

Therefore, the average velocity of the particle is 21{\text{ units}} .

Learn more:  

  • Learn more about the distance between the points <u>brainly.com/question/6278187 </u>
  • 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? <u>brainly.com/question/11801752</u>
  • Learn more about the equivalent fraction <u>brainly.com/question/952259</u>

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.

enot [183]3 years ago
6 0

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  s=6t^2+2t 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.

s(4)=6(4)^2+2(4)=104

s(1)=6(1)^2+2(1)=8

∴ \text{Average Velocity=}\frac{s(4)-s(1)}{4-1}

                            =\frac{104-8}{3}=\frac{96}{3}=32miles/hr

Hence, average velocity is 32 miles/hr.

                                         

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