Distance, displacement

Speed: average speed, instantaneous speed, initial speed, final speed

Velocity: average velocity, instantaneous velocity, initial velocity, final velocity

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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.

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".

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.__