Question

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

Answer 1

`v(6)=6`
`a(6)=2`

Explanation:

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