Question

An object moves along the x axis according to the equation x = 3.00t^2 - 2.00t + 3.00 where x is in meters and t is in seconds.
Determine the average speed between t = 2.00 s and t = 3.00s

Answer 1

                                   x = 3 t²  -  2 t  +  3

When t=2 sec,          x = 3 (4) - 2 (2) + 3
                                     =  12    -   4     + 3  =  11 meters .

When t=3 sec,          x = 3 (9) - 2 (3) + 3
                                     =   27   -   6    +  3  =  24 meters .

Distance = (end position) - (start position) = (24m - 11m) = 13 meters  

Time  =  (end time) - (start time) = (3s - 2s)  =  1 second

Speed  =  (distance) / (time)  =  13 meters / 1 sec  =  13 meters/second

Answer 2

  We are given the equation:

x = 3 t²  -  2 t  +  3
We use that equation to calculate for the distance traveled.

At t=2 sec,          x = 3 (4) - 2 (2) + 3
                             x =11 meters

At t=3 sec,          x = 3 (9) - 2 (3) + 3
                             x = 24 meters

Velocity = (24 meters - 11 meters) / (3 s - 2 s )  = 13 m/s