What Is the Purpose of the Time Interval in Calculating Instantaneous Velocity?

[the_d]

A race car moves such that its position fits the relationship
x(t) = (4.4 m/s) t + (0.91 m/s^3) t^3 (yes cubed)
where x is measured in meters and t in seconds.Approximate the instantaneous velocity at t = 2.6 s, using a time interval of 0.2 s. Answer
in units of m/s.

i am just stuck and don't even know where to start

 

[vincentchan]

ok, the velocity is
$$\frac{\Delta x} {\Delta t}$$

now the question come down to what is delta x and delta t
hope you can come out the answer

 

[dextercioby]

Take the time origin $t_{0}$ to be 0.

Daniel.

 

[the_d]

but what is Xo and X?

 

[dextercioby]

Kay.
$$x_{0}=x(t_{0})=x(0)$$

$$x=x(2.6)$$

Daniel.

 

[the_d]

ok i got all that, but what is still confusing me is the "time interval" what do i do with that

 

[the_d]

Kay.
$$x_{0}=x(t_{0})=x(0)$$

$$x=x(2.6)$$

Daniel.

what is the time interval for?