Aparticle moves according to the equation x = 11t^2, where x is in meters and t is in seconds.

(a) find the average velocity for the time interval from 2.20 s to 2.95 s
(b) find the average velocity for the time interval from 2.20 s to 2.40 s

We are given the equation:

x = 11t^2

We use that equation to calculate for the distance traveled.
For (a)

At t=2.20 sec,    
                             x =53.24 meters

At t=2.95 sec,   
                             x =95.73 meters

Velocity = (95.73 meters - 53.24 meters) / (2.95 s - 2.20 s )  = 56.65 m/s

For (b)

At t=2.20 sec,    
                             x =53.24 meters

At t=2.40 sec,   
                             x =63.36 meters

Velocity = (63.36 meters - 53.24 meters) / (2.40 s - 2.20 s )  = 50.6 m/s