Section 11–2: Speed and Velocity Physical Science Coach Kelsoe Pages 332–337

Objectives Identify appropriate SI units for measuring speed. Compare and contrast average speed and instantaneous speed. Interpret distance–time graphs. Calculate the speed of an object using slopes. Describe how velocities combine.

Speed Speed is the ratio of the distance an object moves to the amount of time the object moves. The SI unit of speed is meters per second (m/s). Choose the unit that makes the most sense! Two ways to express the speed of an object are average speed and instantaneous speed. Both can be useful. Average speed is computer for the entire duration of the trip. Instantaneous speed is measured at a particular instant.

Average Speed Average speed, v, is the total distance traveled, d, divided by the time, t, it takes to travel that distance. This relationship can be illustrated with the following equation: v = d/t During the time an object is moving, its speed may change, but this equation tells you the average speed over the entire trip.

Calculating Average Speed While traveling on vacation, you measure the times and distances traveled. You travel 35 kilometers (21.7 miles) in 0.4 hours, followed by 53 kilometers (32.9 miles) in 0.6 hours. What is your average speed? Total distance (d) = 35 km + 53 km = 88 km Total time (t) = 0.4 h + 0.6 h = 1.0 h Average speed (v) = 88 km/1.0 h = 88 km/h (57 mph)

Instantaneous Speed Average speed is useful because it lets you know how long a trip will take. But when you need to know how fast you are going at a particular moment... ...only instantaneous speed will do! Instantaneous speed, v, is the rate at which an object is moving at a given moment in time.

Graphing Motion A distance-time graph is a good way to describe motion. The slope of the line of the graph is the change distance over the change in time. In its truest sense, the slope of the line gives us the average speed.

Velocity Sometimes speed isn’t descriptive enough to answer a question. You need more information. If we know a cheetah is running at 90 km/h and sees an antelope grazing 30 meters away, can we know when the cheetah will be close enough to attach the antelope? The speed and direction in which an object is moving are called velocity. Velocity is a vector quantity, whereas speed is not.

Velocity Is the only way to change the speed of an object to speed it up or slow it down? Is the only way to change the velocity of an object to speed it up or slow it down? Can an object move with a constant speed but a changing velocity?

Combining Velocities Sometimes the motion of an object involves more than one velocity. Two or more velocities add by vector addition. For instance, if a boat is moving at 30 mph according to its speedometer, and it is floating downstream on a river that is flowing at 5 mph, then its total speed would be 35 mph. If the same boat did a u-turn and continued upstream at the same speed, it’s total speed would be 25 mph.

Combining Velocities How do you find the total velocity if they are not parallel to each other? It’s not as simple as adding or subtracting vectors. If the velocities are perfectly perpendicular, you use Pythagorean theorem to solve for the total velocity. For instance, let’s say a boat was crossing a river with a velocity of 12 mph. If the river was moving at 5 mph, then the boat’s velocity would be 13 mph.

Vocabulary Speed Average speed Instantaneous speed Velocity