Differentiate between distance and displacement

Learning Objectives By the end of this section, you will be able to do the following: • Describe motion in different reference frames • Define distance and displacement, and distinguish between the two • Solve problems involving distance and displacement Section Key Terms displacement distance kinematics magnitude position reference frame scalar vector Defining Motion Our study of physics opens with kinematics—the study of motion without considering its causes. Objects are in motion everywhere you look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. Even in inanimate objects, atoms are always moving. How do you know something is moving? The location of an object at any particular time is its position. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board. In other cases, we use reference frames that are not stationary but are in motion relative to Earth. To describe the position of a person in an airplane, for example, we use the airplane, not Earth, as...

Distance: • Distance is a scalar quantity where there is only magnitude. • It can be measured along any path. • Distance changes according to the path taken. If the path is long, the distance will be also long. Displacement: • Displacement is a vector quantity with both magnitude and direction. • It can only be measured in a straight path. • Displacement depends on the initial and final position of the object and not on its path.

Displacement and Distance are not exactly the same things. I have seen everywhere on the Internet that the derivative of a distance function is it's velocity function, however to my understanding this is not true. The derivative of displacement* is velocity. Is my understanding correct, and what then is the first and second derivative of a distance function. $\begingroup$ Ahmed, people just speak loosely sometimes. I wouldn't worry about it too much unless it's the case that the person is trying to be precise and there is a mismatch in units. In 1D, people quite often use "distance" to mean "signed distance". You usually see more precise language in higher dimensions, i.e. motion in 2D and 3D. $\endgroup$ It's more correct to say that velocity is the derivative of position. It's the instantaneous measure of how position changes with respect to time. The difference between displacement and distance is that distance is a scalar valued function where-as displacement is a vector, it's an arrow. Suppose for example that a particle in $\mathbb^2$ has position: Consider finding the velocity at the black point. Let's measure displacement from the origin (displacement is independent of observer). Velocity is the change of displacement over time. The change in displacement gives the yellow lines below. You can see they are secant lines. Hence in the limit you get the usual derivative: If instead you were to consider distance, you would be computing the length of small arcs centered ...

Distance is a scalar quantity and displacement is a vector quantity. Distance has only magnitude. It measures the actual ground covered. Distance can only be positive. Displacement is measured with reference to a specific point. It is a straight line from the starting point (origin) to the end point. It is therefore also the shortest distance between two points. If the displacement vector is away from the reference point (aka datum) it is often defined as positive and if toward it is defined as negative. It is possible to have an average displacement equal to zero if the object starts and ends in the same position. Displacement is used in considerations of oscillations (including waves). The reference point is the equilibrium position for the oscillator. Displacements above the equilibrium (if above is appropriate) are positive and below the equilibrium are negative.

The difference between distance and displacement is as follows: Distance Displacement It is the length of the path traversed by the object in a certain time. It is the distance travelled by the object in a specified direction in a certain time (i.e. it is the shortest distance between the final and the initial positions). It is a scalar quantity i.e., it has only the magnitude. It is a vector quantity i.e., it has both magnitude and direction. It depends on the path followed by the object. It does not depend on the path followed by the object. It is always positive. It can be positive or negative depending on its direction. It can be more than or equal to the magnitude of displacement. Its magnitude can be less than or equal to the distance, but can never be greater than the distance. It may not be zero even if displacement is zero, but it can not be zero if displacement is not zero. It is zero if distance is zero, but it can be zero if distance is not zero.

What is Displacement? Displacement is considered a vector magnitude and we can describe it as the variation of the position of a body. The displacement focuses on the length of the path of an object that exists considering an initial point and another endpoint. It can be said that the result is a straight line between these two points. Therefore, it should be noted that the displacement does not depend on the path followed by the body in question but as mentioned above the difference between the points considered as initial and final. For example: • If the same person in example # 1, take the tour described above where he leaves his house, travels through a series of places during the day, and finally returns home, considering an initial point like his house and an endpoint his house again, the total displacement of the day will have been 0 meters because the starting and ending point is the same. However, if the displacement of the person from his house to the market is considered, the displacement of the person for that place would be 300 meters. Displacement It is a magnitude that measures the length that is traveled by an object from one point to another. It is a magnitude that measures the variation of the position of a body between two points, considering a starting point and an endpoint. It is considered a scalar magnitude. It is considered a vector magnitude. It depends on the path that the object follows. It does not depend on the path that the object follows. It ...

Suppose the question is somewhat like this: If $v=8-4t$ and the position at time $t= 0\ \rm s$ is $2\ \rm m$, find the distance traveled, displacement, and final position at $t=3\ \rm s$ Since $\text dx/\text dt=v=8-4t$, then $\text dx=(8-4t)\text dt$. After integrating we find $x(t)-2=8t-2t^2$, and substituting the value of $t=3\ \rm s$ we get $x(3)=8\ \rm m$. Is the answer that I found displacement, position or distance? It can't be distance. I am sure of this. But is it position or displacement? Position is a single point. Usually in space we indicate positions with coordinates like $(x,y,z)$ in Cartesian coordinates, $(r,\phi,\theta)$ in spherical coordinates, etc. We can also define the position as a vector, i.e. the position vector, that is a vector that points from the origin (subjectively defined) to the position of the particle in question. It could be $\mathbf r=x\hat x+y\hat y+z\hat z$ using Cartesian coordinates, $\mathbf r=r\hat r$ using spherical coordinates $^*$, etc. In 1D there really isn't anything different between the position coordinate and the position vector, so you don't need to worry about the distinction in the problem you have described in your question. Displacement is the change in position. It is a vector quantity; it is the difference between two position vectors. So, for example, if you go around a circle exactly one time, your displacement over that time is $0$. You can get the displacement at some time $t$ by integrating the instantaneous ...

differences between distance and displacement: • Distance is nothing but the length of the total route travelled by the object during motion. On the other hand, displacement is the least distance between starting and finishing point. • Distance gives the complete information of the path followed by the body. As against this, displacement does not give the complete information of the path travelled by the object. • The value of displacement can be positive, negative or even zero, but the value of the distance is always positive. • Distance is a scalar measure, which takes into account the magnitude only, i.e. we need to specify only the numerical value. Unlike displacement which is a vector measure and takes into account both magnitude and direction. • Distance covered is not the unique path, but the displacement between two locations, is the unique path. • Distance can be calculated by multiplying speed and time. On the contrary, the displacement can be calculated by multiplying velocity and time.

Scalars and vectors are two kinds of quantities that are used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction. Explore some examples of scalars and vectors, including distance, displacement, speed, and velocity. Created by Sal Khan. A vector stores only two parameters of information - length and direction. It doesn't tell you anything about it's origin/location. It can vary with time if it's given as a function of time, for example if the vector symbolises speed of an accelerating object, then it does vary on time, if the speed is constant then it doesn't vary on time. O.K. so on earth we can say that an object is going with velocity v(direction North To South). But what I have learned now is that every point in the universe is the centre of universe. so question 1 Is this true? question 2 if yes than how will you define direction of a particle. I mean that everywhere you are going in the universe you are at the centre of it. Deep questions! 1) Yes, that is a concept from relativity called reference frames. Einstein theorized that the laws of physics should all work no matter what object you think marks the center of the universe, and all experiments up to this point have agreed with him. 2) In a theoretical sense, the vectors you're seeing exist in Euclidean space, which does have a well-identified center (the origin). If someone is doing real-world problems, what you'll find is that they will...