Cross-intercept: represents the initial position at time t=0 Longitudinal intercept: represents the moment when the displacement is zero Slope: The slope of the tangent line at a certain point on the image represents the magnitude of the object's speed. The positive or negative slope of the tangent line at a certain point on the graph represents the direction of the object's speed. The intersection point of the x-t image indicates that the two objects meet Inflection point: indicates a sudden change in the direction of motion of an object

subtopic

Longitudinal intercept: represents the initial velocity of the object Cross-intercept: It means that the object starts timing and then starts to move after a period of time or the object's speed becomes zero after a certain period of time. Image inflection point represents: the moment when the direction of acceleration changes Intersection point: Indicates that two objects have the same speed The area enclosed by the image and the time axis represents the displacement within the corresponding time (note the direction, if the area is represented above the time axis, the displacement direction during this time is the positive direction, if the area is represented below the time axis, the displacement during this time The displacement direction within is the negative direction)

Note: The positive and negative speed represents the direction The v-t image can only describe linear motion, but cannot describe curved motion. The v-t image describes the change of the object's speed with time, but does not represent the movement trajectory of the object.

Longitudinal intercept: represents the acceleration at time t=0 Cross-intercept: represents the moment when the acceleration is zero (the speed at this time is not necessarily zero) Slope: The slope of the tangent line at a certain point represents the rate of change of the object’s acceleration. Area: represents the change in velocity of the object △v

x/t-t image: From x=v0t 1/2 at², we can get x/t=v 0 1/2at, and the slope of the image is a/2

v²-x image: v²-v0²=2ax can get v²=v0² 2ax image slope is 2a

Condition: The object is only affected by gravity and starts falling from rest.

Features: The closer to the equator on the earth, the smaller the acceleration due to gravity; the closer to the poles, the larger the acceleration due to gravity. (The initial velocity is zero and the acceleration is uniformly accelerated linear motion due to gravity)

The process of an object falling freely from rest is a process of free fall motion intercepted from the middle. It is not a free fall motion, but a vertical downward throwing motion.

We can restore the vertical downward motion to free fall motion upwards, and then use the laws of free fall motion to solve the problem

When the object rises to the highest point, the speed is zero, so v0-gt1=0

After the object has gone through the process of rising and falling, the time it takes for it to fall back to the original place is t. The time it takes for the object to rise is t - the falling process, and the time it takes is t2. Then, t 2 = t-t1 (the displacement is zero v0-1 /2gt&sup2=0）

The maximum height of an object rising is the height when the speed decreases to zero, so v=0 (v0&sup2-v&sup2=2gh)

Rise time and fall time (same period)

Speed: the speed at which an object rises and falls through the same point, equal in magnitude and opposite in direction.

The changes in gravitational potential energy in the same section of ascent and descent are equal and equal to mgh

At the same time and in the same place

at the same time and in different places

Same place but different time

different places at different times

b chases a. When the distance between the two objects is X0 and Va=Vb, if xa x0<xb, they can catch up. If xa x0=xb, then there will be no collision. If xa x0>xb, it cannot catch up.

If the object being chased moves in a straight line with uniform deceleration, you should pay attention to determine whether the object has stopped moving before catching up from behind.

If two objects can meet, then when the speed of the two objects is equal, the speed between the two objects has a maximum value

If two objects cannot meet, then when the speed of the two objects is equal, the distance between the two objects has a minimum value

Neither the known quantity nor the unknown quantity involves initial velocity.

Uniformly decelerated linear motion with zero final velocity

Purpose: (1): Further practice the use of dot counters, paper tape data processing and methods of measuring instantaneous speed. (2): Use dotted paper tape to study the movement of the car and analyze the law of the speed of the car changing with time. experiment equipment: A long wooden board with a pulley, a trolley, a thin wire with a small hook, a number of hook codes, a dotting timer, paper tape, a scale, wires, and an AC power supply. Experimental principle: Connect the paper tape to the moving object and pass it through the dot timer. In this way, the points on the paper tape not only record the movement time of the object, but also correspondingly represent the position of the moving object at different times. Study the situation of these points and Can understand the movement of objects. Experimental steps: (1): Place the long wooden board with the pulley on the experimental table, and make the pulley extend out of the table. Fix the dotting timer on the end of the long wooden board without the pulley, and connect the circuit, as shown in Figure 1: (2): Tie a string to the trolley, cross the string across the pulley, and hang a suitable hook underneath. After letting go, see if the car can accelerate and glide balancedly on the wooden board, then pass the paper tape through the dotting timer and fix one end of the paper tape at the back of the car. (3): Stop the car at the dotting timer, turn on the power first, and then release the car to let the car drag the paper tape. The dotting timer will print a row of small dots on the paper tape, and then follow the same method (not Change the number of hook codes) and punch out two paper tapes. Choose the clearest one from these three tapes and record it as tape I. (4): Add a hook code and punch out the paper tape II according to the above method. (5): Reduce one hook code on the basis of the paper tape I, and still press the paper tape III according to the above method. (6): Organize equipment. Precautions: (1) Parallel: The paper tape and string should be parallel to the board. (2) One first, one last: During the experiment, the power should be turned on first, and then the car should be moved; after the experiment, the power should be turned off first and then the paper tape should be taken out. (3) Prevent collisions: Stop the trolley before reaching the end of the long board to prevent the hook code from falling to the ground and the trolley from colliding with the pulley. (4) Reduce errors: The acceleration of the car should be appropriately large to reduce the length measurement error. The acceleration should be enough to clearly pick out ~6 to 7 counting points on a paper tape of about 50cm. (5) Clarify the interval: To distinguish between the points printed by the timer and the manually selected counting points, usually one counting point is taken every four points on the paper tape, that is, the time interval is T=0.02×5s=0.1s. (6) Trace points carefully: It is best to use graph paper when tracing points, and select appropriate units on the vertical and horizontal axes. Trace the points carefully with a thin pencil.

The meaning of the dots on the paper tape: (1): Indicates the position of the object connected to the paper tape at different times. (2): By studying the intervals between points on the paper tape, the movement of the object can be judged. (3): The time interval between counting points can be determined by using the points printed on the paper tape. Selection of paper tape: Choose an ideal paper tape from the three paper tapes, discard some dense points at the beginning, and find a starting point at the back where it is convenient for measurement to determine the counting point. In order to facilitate calculation and reduce errors, the time of five consecutive points is usually used as the time interval, that is, = T = 0.1s. How to collect data: As shown in Figure 2, instead of directly measuring the distance between two counting points, we must first measure the distance from each counting point to the timing zero point, x1, x2, x3, x4... and then calculate the distance between the two adjacent counting points. distance between counting points. Δx1=x1,Δx2=x2−x1,Δx3=x3−x2,Δx4=x4−x3,Δx5=x5−x4.

Average method: The speeds corresponding to the counting points of the paper tape shown in Figure 6, ,,,1,2,3,4,5... are respectively,,,,v1,v2,v3,v4,v5...T is the time between counting points time interval. a1=v2−v1T,a2=v3−v2T,a3=v4−v3T,…,an=vn 1−vnT.a¯=a1 a2 ... ann=(v2−v1) (v3−v2) ... (vn 1−vn)nT=vn 1−vnT From the results, it can be seen that only v1 and vn 1 actually participate in the calculation, and the instantaneous speed of the intermediate points does not play a role in the calculation. Difference-by-difference method: Then: a1=Δx4 Δx13T2, a2=Δx5 Δx23T2, a3=Δx6 Δx33T2, then: a=a1 a2 a33=(Δx4 Δx5 Δx6)−(Δx1 Δx2 Δx3)9T2

v=v0 at

v0, v, and a are all vectors, and the direction of v0 is the positive direction.

x=v0t 1/2at&sup2

v0, a, and x are all vectors, and generally the direction of v0 is the positive direction.

v&sup2 -v 0&sup2=2ax

If v0=0, then v&sup2=2 ax

x=（v0 v）t/2

If v0=0, then x=vt/2

The ratio of instantaneous velocities when continuous equal displacement occurs v1: v2: v3:...: vn=√1: √2: √3:...: √n

The ratio of the time required for the displacement of x, 2x, 3x,...,nx t1:t2:t3:...:tn=√1:√2:√3:...:√n

The ratio of time for continuous equal displacements t1: t2: t3:...: tn=√1: (√2-√1): (√3-√2): (√n-√n-1)

The ratio of the instantaneous speed at the end of T, the end of 2T, the end of 3T, ..., and the end of nT v1: v2: v3: ..., vn=1:2:3:

Within the first T, within the second T, within the second T..., the ratio of the displacements within the nth T x1:x2:x3:...:xn=1²:2²:3²:...:n&sup2

Within the first T, within the second T, within the third T,..., the ratio of the displacements within the nth T x1:x2:x3:...:xn=1:3:5:...:(2n- 1)

Intermediate speed: the instantaneous speed at the middle time = the average speed of an object moving in a straight line at a uniform speed during a period of time = half of the sum of the velocity vectors at the beginning and end of this period of time

Median speed: For an object moving in a straight line at a uniform speed, the speed of the midpoint of the displacement during a period of motion v=√v1² v2²/2

Spark timer

Electromagnetic dotting timer

speed

rate

Linear motion with constant speed and direction

x=vt

The v-t image of uniform linear motion is a straight line parallel to the time axis, and its displacement is numerically equal to the area of ​​the rectangle surrounded by the v-t graph and the corresponding time axis.

Acceleration is the rate of change of velocity

The physical quantity that describes the speed of an object's speed change is a state quantity.

Definition: a=△v/△t

Unit: m/s²

Acceleration is a vector whose direction is consistent with the direction of velocity change.

Determined by F combined/m

time interval

time

distance

Displacement

Used to replace the point where the object has mass

When studying the motion of an object, if the shape and size of the object have negligible influence on the object under study, it can be regarded as a particle.

Reference System

Coordinate System