Every measurement of time involves measuring a change in some physical quantity. It may be a number on a digital clock, a heartbeat, or the position of the Sun in the sky. In physics, the definition of time is simple— time is change , or the interval over which change occurs.
It is impossible to know that time has passed unless something changes. The amount of time or change is calibrated by comparison with a standard. The SI unit for time is the second, abbreviated s. We might, for example, observe that a certain pendulum makes one full swing every 0. We could then use the pendulum to measure time by counting its swings or, of course, by connecting the pendulum to a clock mechanism that registers time on a dial. This allows us to not only measure the amount of time, but also to determine a sequence of events.
How does time relate to motion? We are usually interested in elapsed time for a particular motion, such as how long it takes an airplane passenger to get from his seat to the back of the plane.
To find elapsed time, we note the time at the beginning and end of the motion and subtract the two. For example, a lecture may start at A. Life is simpler if the beginning time t 0 is taken to be zero, as when we use a stopwatch. If we were using a stopwatch, it would simply read zero at the start of the lecture and 50 min at the end. Your notion of velocity is probably the same as its scientific definition.
You know that if you have a large displacement in a small amount of time you have 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 displacement change in position divided by the time of travel ,. If the starting time t 0 is taken to be zero, then the average velocity is simply.
Notice that this definition indicates that velocity is a vector because displacement is a vector. It has both magnitude and direction. His average velocity would be. The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals.
Figure 2. A more detailed record of an airplane passenger heading toward the back of the plane, showing smaller segments of his trip. The smaller the time intervals considered in a motion, the more detailed the information.
When we carry this process to its logical conclusion, we are left with an infinitesimally small interval. Over such an interval, the average velocity becomes the instantaneous velocity or the velocity at a specific instant. Police give tickets based on instantaneous velocity, but when calculating how long it will take to get from one place to another on a road trip, you need to use average velocity. Instantaneous velocity v is the average velocity at a specific instant in time or over an infinitesimally small time interval.
Mathematically, finding instantaneous velocity, v , at a precise instant t can involve taking a limit, a calculus operation beyond the scope of this text.
However, under many circumstances, we can find precise values for instantaneous velocity without calculus. In physics, however, they do not have the same meaning and they are distinct concepts. One major difference is that speed has no direction. Sometimes the data might look insufficient so check if some equations have to be solved simultaneously.
Thank you so much physicsquest! The analogy of one person running towards the other standing still helped it make sense for me.
I did much better on the rest of my homework than I did on this one problem, I found a great site that helped me to do just what you said, figure out what I'm given and pick an equation based on which ONE variable I don't have.
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