Position of the body at x=t²-6t+5 find average velocity and average speed and acceleration at t= 6sec ?

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Answer 1 · 2018-02-17T21:15:44

$v (6) = 6$ $v(6)=6$
$a (6) = 2$ $a(6)=2$

The relation between position, velocity and acceleration is

$a(t)=v'(t)=x''(t)$

We will start by determine the velocity and acceleration

Position function

$x(t)=t^2-6t+5$

The derivative of the position function is the velocity function

$x'(t)=v(t)=2t-6$

The derivative of the velocity function is the acceleration function

$v'(t)=a(t)=2$

Note

Average velocity or acceleration refers to a change in a time period

** Instantaneous ** velocity or acceleration refers to a single point in time

To find the instantaneous velocity and acceleration plug in $t=6$

Instantaneous velocity

$v(6)=2*6-6=6$

Instantaneous acceleration

$a(6)=2$

We miss some units, but to determinate these we need to know a bit more about the problem