PS-5.1 Explain the relationship among distance, time, direction, and the velocity of an object.
Speed: average speed, instantaneous speed, initial speed, final speed
Velocity: average velocity, instantaneous velocity, initial velocity, final velocity
In Physics there are two kinds of measurements you should be able to recognize, scalar measurements and vector measurements. Scalar measurements are all measurements that can be expressed as a quantity without a direction. Some examples of scalar measurements are distance, time, temperature, volume & etc. Vector measurements have a quantity AND a direction. Some examples of vector measurements are displacement, velocity, acceleration, and force. All of these vector measurements must have a direction associated with them.
Simply put, distance can be defined as the total length of a path that an object travels. For instance, if you were to drive from Myrtle Beach to Charleston your distance would be about 160km. Turn around and and drive back, and your total distance would be 320km. Note that in both cases there is no direction associated with the distance measurement.
Myrtle Beach -----------------------------160km---------------------------------------------> Charleston
Displacement is not the same as distance. Displacement is the straight line distance and direction between your starting an ending point. Refer back to the last example and you can see that our drive from Myrtle beach to Charleston would result on a displacement of 160km South. Displacement is a vector, it must have a direction. Remember that displacement is the straight line distance and direction between starting and ending points? If we turn around in Charleston and drive back to Myrtle beach we find that our displacement is 0km, because our starting and ending points are the same. Here is another example of the difference between distance and displacement.
The diagram above shows the path that Ashley traveled during the Bike-a-Thon. The total distance she traveled is found by simply adding up each leg of the trip between the starting point at X and the ending point at "Y".
dtotal = 10km + 3km + 3km + 3.5km + 8km + 4.5km = 32km
The total distance Ashley rode was 32km. However, refer to the diagram below and you can clearly see that Ashley's Displacement was 3km South East.
Speed is a measure of how fast an object is traveling. Another way to say this is that speed is the rate of change in position or the rate of motion. Speed is calculated using the distance traveled and the time of motion. If Ashley rode from point "X" to point "Y" in 6.4hours, then her speed would be calculated as follows.
Her average speed was 5km/h. The little line above the S in the problem above means that this speed calculated here is an average speed. Average speed encompasses the entire trip. Her speed may have been different at different points during the ride, but the average for the entire trip was 5km/h. Since speed is calculated using distance, speed is a scalar measurement. In most cases you will deal with average speed. Automobile speedometers give an instantaneous speed, that is the speed at an instant or point in time.
Now lets calculate Ashley's velocity for the ride. Velocity is defined as rate of motion in a given direction. Since the calculation of velocity uses displacement rather than distance, velocity is a vector measurement, meaning it has a quantity and associated direction. Here is the velocity calculation.
Note the big difference in the value of the answer. The difference comes from the fact that the Displacement, 3km, is much different than the distance, 32km, in the previous problem. Also note that the direction is given in the answer. Again, the little line above the "V" indicates that this is an average velocity rather than an instantaneous velocity. An instantaneous velocity is the velocity at a given "point" or instant in time. In most cases you will deal with average velocity. Automobile speedometers give an instantaneous velocity. It is important to remember that because the velocity has a direction, a change in either the speed or the direction results in a change in velocity. This leads to an interesting fact, a car going around a curve can have a constant speed and yet still have a changing velocity. The car in the following diagram is traveling around a curve. Suppose the driver looks at his speedometer when the car is at points "A", "B", and "C". At each of these points he notices that the speedometer reads 30km/h. His speed is a constant 30km/h as he rounds the curve. Now look at what is happening to his direction of motion. As he goes around the curve, his direction changes from East to South. Because of this change in direction, we have to conclude that his velocity is changing even though his speed is constant.