Respuesta :
Answer:
Average velocity is 21 miles/hr
Step-by-step explanation:
Given a particle moving away from its initial position
Position after t hours that is
s(t) = 4[tex](t^{2})[/tex] + t
We have to find the average velocity of the particle over the interval [1,4]
Average velocity = [tex]\frac{Distance Travelled}{Time Elapsed}[/tex]
Distance travelled = [tex] [s]_{1}^{4}[/tex]
= s(4) - s(1)
= 4[tex](4^{2})[/tex] + 4 - 4[tex](1^{2})[/tex] -1
= 63 miles
Time elapsed = 4 - 1 = 3
Average velocity = [tex]\frac{63}{3}[/tex]
= 21 miles/hr
The average velocity of the moving 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] and the interval is [tex]\left[{1,4}\right][/tex] .
Step by step explanation:
Step 1:
The given position of the particle after [tex]t[/tex] hours is [tex]s\left(t\right)=4{t^2}+t[/tex] .
First find the distance travelled in the interval of [tex]\left[{1,4}\right][/tex] .
The distance travelled by the moving particle in a line 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 moving particle in a line 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}+4\hfill\\s\left(1\right)=68\hfill\\\end{gathered}[/tex]
Now evaluate the total distance travelled by the moving particle in the given 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 provided interval is [tex]\left[{1,4}\right][/tex] .
Now the time can be calculated as,
[tex]\begin{aligned}{\text{time elapsed}}&=4-1\\&=3\\\end{aligned}[/tex]
Step 3:
Now we evaluate the average velocity of the moving particle.
The average velocity can be evaluated as,
[tex]\begin{aligned}{\text{average velocity}}&=\frac{{{\text{distance travelled}}}}{{{\text{time elapsed}}}}\\&=\frac{{63}}{3}\\&=21{\text{units}}\\\end{aligned}[/tex]
Thus, the average velocity of the moving particle is [tex]21{\text{ units}}[/tex] .
Learn more:
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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.
