Simonds Portland Community College Given Information Gino drove exactly 60 miles between 3 PM and 4 PM. Question How fast was Gino driving right at 3:30 PM? How the heck should I know? We know that Gino’s average speed over the entire hour was 60 mph but we have absolutely no idea what his instantaneous speed was at any time during that hour.

Simonds Portland Community College Definition The average velocity of an object moving along a numbered line is: Change in position Elapsed time =  p(t) p(t)  t

Simonds Portland Community College 100 ft 80 ft 60 ft 40 ft 20 ft 0 ft P(1 sec)  54 ft P(0 sec)  0 ft P(2 sec)  72 ft The average velocity over the first second was 54 ft/sec. The average velocity over the second second was 18 ft/sec. What was the instantaneous velocity exactly 1 second into the flight? Definition The average velocity of an object moving along a numbered line is: Change in position Elapsed time =  p(t) p(t)  t

Simonds Portland Community College Definition The instantaneous velocity of an object moving along a numbered line is:  p(t) p(t)  t lim  t ft/sec[54, ][1, 1.01] 36.4 ft/sec[54, 57.64][1, 1.1] 18 ft/sec[54, 72][1, 2] Average Velocity Positions (ft) Time interval (sec) 100 ft 80 ft 60 ft 40 ft 20 ft 0 ft P(1 sec)  54 ft P(0 sec)  0 ft P(2 sec)  72 ft The average velocity over the first second was 54 ft/sec. The average velocity over the second second was 18 ft/sec. What was the instantaneous velocity exactly 1 second into the flight?