The sketch shows a ball rolling at constant velocity along a level floor. The ball rolls from the first position shown to the second in 1 second. The two positions are 1 meter apart. Discuss with your partner where you would sketch the ball at successive 1-second intervals all the way to the wall (neglect resistance).

Would the successive ball positions be evenly spaced, farther apart, or closer together?
Why?

The ball reaches the wall with a speed of m/s and takes a time of seconds.

An object starting from rest galns a speed v = at when it undergoes uniform acceleration. The distance it covers is d = ½at². Uniform acceleration occurs for a ball rolling down an inclined plane. The plane below is tilted so a ball picks up a speed of 2 m/s each second; then its acceleration a 2 m/s². The positions of the ball are shown for 1-second intervals. Complete the six blank spaces for distance covered, and the four blank spaces for speeds.

distance	speed

Do you see that the total distance from the starting point increases as the square of the time? This was discovered by Galileo. If the incline were to continue, predict the ball's distance from the starting point for the next 3 seconds.

Note the increase of distance between ball positions with time. Do you see an odd-integer pattern (also discovered by Galileo) for this increase? If the incline were to continue, predict the successive distances between ball positions for the next 3 seconds.