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Measure the length of your path from the starting position to the second marked position. Multiply this measurement by the total number of times you walked across the floor. Then add this number to your measurement from step 6. Compare the two measurements from steps 6 and 7.
Kilometer: km: 10 3 m: About 6/10 mile: hecto: h: 10 2: Hectoliter: hL: 10 2 L: 26 gallons: deka: da: 10 1: Dekagram: dag: 10 1 g: Teaspoon of butter: 10 0 (=1) deci: d: 10 –1: Deciliter: dL: 10 –1 L: Less than half a soda: centi: c: 10 –2: Centimeter: cm: 10 –2 m: Fingertip thickness: milli: m: 10 –3: Millimeter: mm: 10 –3 m: Flea ...
Electric Current. meter (m) kilogram (kg) second (s) ampere (A) Table 1.1 Fundamental SI Units. It is an intriguing fact that some physical quantities are more fundamental than others and that the most fundamental physical quantities can be defined only in terms of the procedure used to measure them.
- Overview
- What does velocity mean?
- What does speed mean?
- What do solved examples involving velocity and speed look like?
Velocity or speed? Instantaneous or average? Keep building your physics vocabulary.
What does velocity mean?
Your notion of velocity is probably similar to its scientific definition. You know that a large displacement in a small amount of time means a large velocity and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.
Average velocity is defined to be the change in position divided by the time of travel.
vavg=ΔxΔt=xf−x0tf−t0
In this formula, vavg is the average velocity; Δx is the change in position, or displacement; and xf and x0 are the final and beginning positions at times tf and t0 , respectively. If the starting time t0 is taken to be zero, then the average velocity is written as below:
Your notion of velocity is probably similar to its scientific definition. You know that a large displacement in a small amount of time means a large velocity and that velocity has units of distance divided by time, such as miles per hour or kilometers per hour.
Average velocity is defined to be the change in position divided by the time of travel.
vavg=ΔxΔt=xf−x0tf−t0
In this formula, vavg is the average velocity; Δx is the change in position, or displacement; and xf and x0 are the final and beginning positions at times tf and t0 , respectively. If the starting time t0 is taken to be zero, then the average velocity is written as below:
vavg=Δxt
Note: t is shorthand for Δt .
In everyday language, most people use the terms speed and velocity interchangeably. In physics, however, they do not have the same meaning, and they are distinct concepts. One major difference is that speed has no direction. Thus, speed is a scalar. Just as we need to distinguish between instantaneous velocity and average velocity, we also need to distinguish between instantaneous speed and average speed.
Instantaneous speed is the magnitude of instantaneous velocity. For example, suppose the airplane passenger at one instant had an instantaneous velocity of −3.0ms , the negative meaning toward the rear of the plane. At that same time his instantaneous speed was 3.0ms . Or suppose that at a particular instant during a shopping trip, your instantaneous velocity is 40kmhr due north. Your instantaneous speed at that instant would be 40kmhr —the same magnitude but without a direction. Average speed, however, is very different from average velocity. Average speed is the distance traveled divided by elapsed time. So, while the magnitudes of the instantaneous speed and velocity are always identical, the magnitudes of average speed and velocity can be very different.
Since distance traveled can be greater than the magnitude of displacement, the average speed can be greater than the magnitude of the average velocity. For example, if you drive to a store and return home in half an hour and your car’s odometer shows the total distance traveled was 6 km, then your average speed was 12kmhr . Your average velocity, however, was zero because your displacement for the round trip is zero—Displacement is change in position and, thus, is zero for a round trip. Thus average speed is not simply the magnitude of average velocity.
Another way of visualizing the motion of an object is to use a graph. A plot of position or of velocity as a function of time can be very useful. For example, for this trip to the store, the position, velocity, and speed-vs.-time graphs are displayed in Figure 3. Note that these graphs depict a very simplified model of the trip. We are assuming that speed is constant during the trip, which is unrealistic given that we’ll probably stop at the store. But for simplicity’s sake, we will model it with no stops or changes in speed. We are also assuming that the route between the store and the house is a perfectly straight line.
Example 1: Disoriented iguana
An iguana with a poor sense of spatial awareness is walking back and forth in the desert. First the iguana walks 12 meters to the right in a time of 20 seconds. Then the iguana runs 16 meters to the left in a time of 8 seconds. What was the average speed and average velocity of the iguana for the entire trip? Assume that rightward is the positive direction. To find the average speed we take the total distance traveled divided by the time interval. average speed=distance traveledtime interval=12.0 m+16.0 m20.0 s+8.0 s average speed=28.0 m28.0 s average speed=1 m s To find the average velocity we take the displacement Δx divided by the time interval. average velocity=displacementtime interval=−4.0 m28.0 s average velocity=−17 m s [How did we find the displacement?]
Example 2: Hungry dolphin
A hungry dolphin is swimming horizontally back and forth looking for food. The motion of the dolphin is given by the position graph shown below. Determine the following for the dolphin: a. average velocity between time t=0 s to t=6 s b. average speed between t=0 s to t=6 s c. instantaneous velocity at time t=1 s d. instantaneous speed at time t=4 s Part A: Average velocity is defined to be the displacement per time. vavg=ΔxΔt=0 m−8 m6 s−0 s=−8 m6 s(Use definition of average velocity.) vavg=−43ms(Calculate and celebrate.) Part B: Average speed is defined to be the distance traveled per time. The distance is the sum of the total path length traveled by the dolphin, so we just add up all the distances traveled by the dolphin for each leg of the trip. vavg=distance traveledΔt=12 m+0 m+4 m6 s−0 s=16 m6 s(use definition of average speed) [How do you determine the distance?] vavg=83ms(calculate and celebrate) Part C: Instantaneous velocity is the velocity at a given moment and will be equal to the slope of the graph at that moment. To find the slope at t=1s we can determine the "rise over run" for any two points on the graph between t=0s and t=3s (since the slope is constant between those times). Choosing the times t=2s and t=0s , we find the slope as follows, vinstantaneous=slope=x2−x0t2−t0 vinstantaneous=0 m−8 m2 s−0 s=−8 m2 s vinstantaneous=−4ms [How did we find the instantaneous velocity?] Part D: Instantaneous speed is the speed at a given moment in time and will be equal to the magnitude of the slope. Since the slope at t=4s is equal to zero, the instantaneous speed at t=4s is also equal to zero. [Attributions and References]
M: 10 6: megacurie: MCi: 10 6 Ci: high radioactivity: kilo: k: 10 3: kilometer: km: 10 3 m: about 6/10 mile: hecto: h: 10 2: hectoliter: hL: 10 2 L: 26 gallons: deka: da: 10 1: dekagram: dag: 10 1 g: teaspoon of butter — — 10 0 (=1) deci: d: 10-1: deciliter: dL: 10-1 L: less than half a soda: centi: c: 10-2: centimeter: cm: 10-2 m ...
Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and direction. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use.
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Section Summary. Physical quantities are a characteristic or property of an object that can be measured or calculated from other measurements. Units are standards for expressing and comparing the measurement of physical quantities. All units can be expressed as combinations of four fundamental units.
