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

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;

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,

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

Then,

The average speed of the particle over interval 2 is,

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

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,

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.

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The average speed of this particle over the interval 2<t<10 is 32 m/s.

Step-by-step explanation:

The position of a particle is given by :

Where t is time in seconds

We need to find the average speed of this particle over the interval 2<t<10

Let v is the velocity of a particle

At t = 2 s,

v₂ = 4(2) + 1 = 9 m/s

At t = 10 s,

v₁₀ = 4(10) + 1 = 41 m/s

The average speed of this particle over the interval 2<t<10 is :

v=v₁₀-v₂

= 41 m/s - 9 m/s

= 32 m/s

So, the average speed of this particle is 32 m/s.

5.6%

step-by-step explanation: