What is the average speed, over the first 3.0 s of its motion, of a pebble released from rest off a bridge?

Our first step in this problem would be to find the speed of the pebble at solid intervals, so let's work on finding its speed after every second starting with t=0.

To do this, let's find a motion equation that we can use. The first one that comes to mind is Vf = Vi + a*t. From the problem, we know that the pebble is released from rest (so Vi = 0, and a = 9.8 m/s²), and we already know the time intervals we want to break it up into, so our best option would be to make a chart listing the speeds at the end of each second.

When t = 0, Vf = 0 m/s

When t = 1, Vf = 9.8 m/s

When t = 2, Vf = 19.6 m/s

When t = 3, Vf = 29.4 m/s

Then, you should just be able to average out the velocities and divide by four to get an average speed of 14.7 m/s!