Average Value of a Fnc & Motion

A bug is moving along a straight path over the interval  $0\le t\le8$ seconds. The velocity of the bug in, inches/second, is given in the graph below. The areas bounded by the x-axis and the graph of velocity are 6 and 4 respectively as shown on the graph. The initial position of the bug is given by  $s\left(0\right)=3$ . Find the position of the bug after 8 seconds.

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Average value of the function  $f\left(t\right)=t\sin\left(t^2\right)$  on the interval  $\left[0,10\right]$  is

A bug is moving along the x-axis on the interval [0,10] seconds. The velocity of the bug at time t is given      
by the equation  $v\left(t\right)=2t-2$ where v(t) is measured in meters/second. The average velocity, in cm/s, of the bug over the interval  $0\le t\le10$ is

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

A particle is moving along a straight path and its velocity is modeled by the below graph. At which point is the speed of the particle increasing?

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Tags

CCSS.HSF.IF.B.4

Find the average value of the function f, whose graph is shown below, on the interval [0,8].

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• $\frac{\ 9\ }{8}$

• $\frac{\ 10\ }{8}$

A bug is moving in a linear path with its velocity given by  $v\left(t\right)=4t^3-3t^2+4t$ when  $0\le t\le8$ . The bug is at position 3 when t=0. Find the position of the bug at time t=1. 

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