Question

A particle travels along the x axis such that it’s position at time t is given by the function x(t)=2t+t. What is the average speed of this particle over the interval 2

Answer 1

The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

Given that,

A particle travels along the x-axis such that its position at time t is given by,

Function; $\rm x(t)=2t^2+t$

We have to find,

What is the average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10?

According to the question,

The position of the particle is given by,

$\rm x(t)=2t^2+t$

The average speed of this particle is determined by differentiating the function with respect to x,

$\rm \dfrac{dx}{dt} = \dfrac{d(2t^2+t)}{dx}\\\\\dfrac{dx}{dt} = 4t + 1 \\\\v(t) = 4t+1$

Then,

The average speed of the particle over interval 2 is,

$\rm v(t) = 4t+1 \\\\v(2) = 4(2)+1\\\\v(2) = 8+1 \\\\v(2) = 9 \ meter \ per \ second$

And the average speed of the particle over interval 10 is,

$\rm v(t) = 4t+1 \\\\v(10) = 4(10)+1\\\\v(10) = 40+1 \\\\v(10) = 41 \ meter \ per \ second$

Therefore,

The average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is,

$\rm v(t) = v(10)-v(2)\\\\v(t) = 41-9\\\\v(t)= 32 \ meter \ per \ second$

Hence, The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

For more details refer to the link given below.

https://brainly.com/question/2292357