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

1 Answer
Feb 17, 2018

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