What is the formula for calculating displacement? Derivation of the displacement formula

Calculation formula: x=x2-x1 (last position minus initial position).

It should be noted that:

Displacement is a straight-line distance, not a distance. (δx is the displacement, x1 is the initial position, and x2 is the last position).

In the International System of Units.

si), the principal unit of displacement is: meters. In addition: centimeters, kilometers, etc. The displacement formula of uniform variable speed motion is: x=v0t+1 2·at 2

Note: v0 is the initial velocity, t is the time, and a is the acceleration.

Extended information: Displacement

As shown in the figure, when the instantaneous T particle is located at the q point and the instantaneous T + T is located at the q point, the vector represents the displacement of the particle from the T time interval in the T time interval. It is equal to the difference between the sagittal diameter of point q and the sagittal diameter of point q, i.e., r=r(t+ t) r(t).

At the same time, the particle moves along the trajectory curve by the q point in the t time interval.

To Q, the distance traveled is arc length.

scalar). Therefore, displacement and distance are two different concepts. When t is small, the difference between the modulus and the distance of the displacement vector is a small-order quantity. When t 0, the two are equal.

Practice question: The military training team of a middle school is at a constant speed, and the instructor rides a bicycle to send the lagging Xiao Wang from the end of the team to the front of the team, and then returns immediately. By the time the instructor returned to the end of the team, the team had advanced 200m, and the magnitude of the instructor's displacement throughout the process was

M Answer: 200

Description] The distance traveled is displacement, so 200m

If an object moves from the initial position to the last position in a certain period of time, the directed line segment from the initial position to the last position is called the displacement. Its magnitude is the straight-line distance from the initial position to the last position of the moving object; The direction is from the beginning position to the last position. The displacement is only related to the beginning and end position of the object's motion, not the trajectory of the motion.

If the particle returns to its original position after a period of time during motion, then the distance is not zero and the displacement is zero.

x=x2-x1 (last position minus initial position).

It should be noted that:

Displacement is a straight-line distance, not a distance.

In the International System of Units (SI), the principal unit of displacement is: meters. In addition: centimeters, kilometers, etc. The displacement formula of uniform variable speed motion is: x=v0t+1 2·at 2

Inference of the velocity and displacement of the uniform variable velocity: x=vot+ at Note: v0 refers to the initial velocity vt refers to the final velocity.

The formula for the displacement of a uniform accelerating linear motion with zero initial velocity is derived:

Since the average velocity of linear motion at uniform variable speed v(average)=(v0+vt) 2v0=0, v(average)=vt 2 is substituted into s=v(average)t, that is, s=(vt)t 2

And vt=at

So s=att 2=at2 2

Direction of displacement vs. direction of velocityThe direction of velocity is not directly related to the direction of displacement, and only in a linear motion without return (i.e., moving in one direction), the direction of velocity must be the same as the direction of displacement. In addition to this, the direction of velocity may or may not be the same as the direction of displacement.

For example, in a vertical upward throwing motion, when the object rises, the direction of velocity (upward) is the same as the direction of displacement (upward), and the direction of velocity (downward) is opposite to the direction of displacement (upward) before falling back to the throwing point during the falling process. Therefore, it is necessary to judge on a case-by-case basis.

High school can be sought with an average pace of time.

The velocity is defined according to the acceleration, the acceleration is uniform, the acceleration increment of t time is at, the final velocity v=vo+at, the average velocity of uniform acceleration is (vo+v) 2 is substituted into v=vo+at, and the average velocity is (vo+at 2), and the displacement: s=(vo+at2) t=vot+(1 2)at 2.

x = v0 t + 1/2) a t^2

Calculus is used to derive this formula. For those who have studied calculus, the derivation process is as easy as 1+2=3. Since the landlord raised this question, the landlord probably hasn't studied calculus yet, right?

In high school physics, you should have learned such a basic knowledge:

Make a v-t function image. Then the area of the graph enclosed by x=t0, x=t, x-axis, and the v-t curve is the displacement from t0 to t. If part of the enclosed graph is below the x-axis, the area of that part is negative, and for the part above the x-axis, the area is positive.

For uniform variable speed linear motion, v = v0 + at

To do the v --t function image, v is the y-axis and t is the x-axis.

The v --t image is a straight line.

v0 is the intercept on the y-axis, and v0 > 0 may be set to v0.

a is the slope of the straight line. Let's assume a > 0.

The shape enclosed by x=0, x=t, x-axis, and the line v=v0+at is a right-angled trapezoid.

The height of the trapezoid is t

The top bottom of the trapezoid is v0

The bottom of the trapezoid is V0+AT

The area of the trapezoid is (v0 + v0 + at)*t 2 = v0t + 1 2)at 2

Therefore displacement s = v0t + 1 2)at 2

Calculation formula:

x=x2-x1 (last position minus initial position) It should be noted that the displacement of this hand is a straight-line distance, not a distance. (δx is the displacement, x1 is the initial position, and x2 is the last position).

In the International System of Units.

si), the principal unit of displacement is: meters. In addition: centimeters, kilometers, etc. The displacement formula of uniform variable speed motion is: x=v0t+1 2·at 2

Note: v0 is the initial velocity, t is the time, and a is the acceleration.

Introduction to the concept of displacement

As shown in the figure, the instantaneous T particle is located at the Q point, and the instantaneous T + T is located at the Q point, then the vector represents the displacement of the particle in the T time interval from the T time. It is equal to the difference between the sagittal diameter of point q and the sagittal diameter of point q, i.e., r=r(t+ t) r(t).

At the same time, the particle moves along the trajectory curve by the q point in the t-time trace clearance interval.

To Q, the distance traveled is arc length.

scalar). Therefore, displacement and distance are two different concepts. When t is small, the difference between the modulus and the distance of the displacement vector is a small-order quantity. When t 0, the two are equal.

The displacement calculation formula is Danpei ridge: δx=x2-x1 (the last position minus the initial position) It should be noted that the displacement is a straight line distance, not a distance. (δx is the displacement, x1 is the initial position, and x2 is the last position).

In the SI mold osmosis (SI), the principal unit of displacement is: meter. In addition: centimeters, kilometers, etc. The displacement formula of uniform variable speed motion is: x=v0t+1 2·at 2

Note: v0 is the initial velocity, t is the time, and a is the acceleration.