# The displacement (in meters) of a particle moving in a straight line is given by s = -5t + 17,...

## Question:

The displacement (in meters) of a particle moving in a straight line is given by {eq}s =t^2 -5t + 17, {/eq} where {eq}t {/eq} is measured in seconds

(a) Find the average velocity over each time interval.

{eq}(1) \ \ (3,4) \\ (2) \ \ (3.5,4) \\ (3) \ \ (4,5) \\ (4) \ \ (4,4.5) {/eq}

(b) Find the instantaneous velocity when {eq}t = 4 {/eq}

## Average value :

Average value of function is also known as mean of function.

Consider a function {eq}\displaystyle f(x) {/eq} .Then average value of the function {eq}\displaystyle f(x) {/eq} on the interval {eq}\displaystyle [a,b] {/eq} is given by

Average value {eq}\displaystyle = \frac{\int_a^bf(x)dx}{b-a} {/eq}

Given displacement function is {eq}\displaystyle s = t^2 -5t + 7 {/eq}

On derivating both sides , we get velocity

Then Average value of function is...

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