Velocity - The rate at which the position of an object changes with time in a particular direction. There are two ways we discuss velocity. Average velocity - estimated velocity over a relatively large time interval. Instantaneous velocity - velocity at a particular instant of time (or over infinitesimally small time interval). Average velocity displacement total distance traveled total time time interval Average speed Average velocity in the x-direction Velocity is a vector quantity – requires magnitude and direction Speed is a scalar quantity – only has magnitude The average speed and the average velocity do not have to be the same!! When you use average velocity it does not mean the velocity is constant!! The average velocity contains no information about any fluctuations that occur in the instantaneous velocity.

Instantaneous velocity The instantaneous velocity can be determined by differentiating the expression that describes the position as a function of time. The time interval over which we are looking becomes infinitesimally small Units: [s] = [v] = m/s, km/hr, mi/hr, cm/s, etc. When discussing instantaneous velocity speed is the magnitude of the instantaneous velocity. Typically we will be using instantaneous velocity not average velocity, so from now on whenever we are discussing instantaneous velocity we will jus say velocity. Example:

Start x0 = 0 Example: 100 Yards What is the average speed of the football player in the situation above if it takes 5 minutes to go from start to finish? What is the average velocity of the football player in the situation above if it takes 5 minutes to go from start to finish? To the right t = 5 min = 300 s To the right What is the instantaneous velocity of the football player at the opposite goal line? The football player must stop moving forward and begin moving in the reverse direction. v = 0 ft/s

A person initially at point P in the illustration stays there a moment and then moves along the axis to Q and stays there a moment. She then runs quickly to R, stays there a moment, and then strolls slowly back to P. Which of the position vs. time graphs below correctly represents this motion? Answer: 2.

The bird is traveling twice as fast as the runner. A marathon runner runs at a steady 15 km/hr. When the runner is 7.5 km from the finish, a bird begins flying from the runner to the finish at 30 km/hr. When the bird reaches the finish line, it turns around and flies back to the runner, and then turns around again, repeating the back-and-forth trips until the runner reaches the finish line. How many kilometers does the bird travel? 1. 10 km 2. 15 km 3. 20 km 4. 30 km The bird is traveling twice as fast as the runner. Answer: 2. It takes the runner half an hour to reach the finish.

Acceleration - The rate at which the velocity of an object changes with time in a particular direction. We also discuss acceleration in two ways: Average acceleration - estimated acceleration over a relatively large time interval. Instantaneous acceleration - acceleration at a particular instant of time (or over infinitesimally small time interval). Average acceleration change in velocity in the x-direction Would a negative acceleration correspond to an increase or a decrease in the speed of an object? It depends on the direction of the velocity. A negative acceleration means that there is an acceleration directed in the negative of the coordinate direction. time interval Average acceleration in the x-direction Instantaneous acceleration We will primarily discuss constant acceleration cases, but this is the general definition of acceleration. Units: [a] = m/s2, km/hr2, mi/hr2, cm/s2, etc. Do not mix time units!! – km/shr