Is it possible to know the instantaneous speed of a person

To illustrate this idea mathematically, we need to express position x as a continuous function of t denoted by x t. The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t :.

Like average velocity, instantaneous velocity is a vector with dimension of length per time. The slope of the position graph is zero at this point, and thus the instantaneous velocity is zero. If the position function had a minimum, the slope of the position graph would also be zero, giving an instantaneous velocity of zero there as well. Thus, the zeros of the velocity function give the minimum and maximum of the position function. Figure 3. Given the position-versus-time graph of Figure , find the velocity-versus-time graph.

Notice that the object comes to rest instantaneously, which would require an infinite force. Thus, the graph is an approximation of motion in the real world. The graph contains three straight lines during three time intervals. We find the velocity during each time interval by taking the slope of the line using the grid. Show Answer. Time interval 0. Time interval 1.

During the time interval between 0 s and 0. In the subsequent time interval, between 0. From 1. The object has reversed direction and has a negative velocity. In everyday language, most people use the terms speed and velocity interchangeably.

In physics, however, they do not have the same meaning and are distinct concepts. One major difference is that speed has no direction; that is, speed is a scalar. We can calculate the average speed by finding the total distance traveled divided by the elapsed time:. Average speed is not necessarily the same as the magnitude of the average velocity, which is found by dividing the magnitude of the total displacement by the elapsed time.

Specific information is available there on the following topic:. Physics Tutorial. My Cart Subscription Selection. Instantaneous Speed. You're pretty motivated to get home, so say you start running at six meters per second. Maybe it's been a while since the last time you ran, so you have to slow down a little bit to two meters per second. When you get a little closer to home, you say: "No, Captain Antares wouldn't give up "and I'm not giving up either", and you start running at eight meters per second and you make it home just in time for the opening music.

These numbers are values of the instantaneous speed. The instantaneous speed is the speed of an object at a particular moment in time. And if you include the direction with that speed, you get the instantaneous velocity. In other words, eight meters per second to the right was the instantaneously velocity of this person at that particular moment in time. Note that this is different from the average velocity.

If your home was 1, meters away from school and it took you a total of seconds to get there, your average velocity would be five meters per second, which doesn't necessarily equal the instantaneous velocities at particular points on your trip.

In other words, let's say you jogged 60 meters in a time of 15 seconds. During this time you were speeding up and slowing down and changing your speed at every moment. Regardless of the speeding up or slowing down that took place during this path, your average velocity's still just gonna be four meters per second to the right; or, if you like, positive four meters per second.

As the gun goes off, she trips and falls down. It takes her several seconds to recover, but she finally gets up and sprints toward the finish line. Just before the finish line, she falls again, recovers, and finishes the race. Total time is 40 seconds. What was her average speed? But what does this mean?