How to prove that the instantaneous velocity in the middle of a process is equal to the average velocity of the process, that is, vzhong = 1 / 2 [V0 + VT]

We can use the image method
Draw the V / t image, and then you can follow the ladder
The median line of a shape is equal to half the length of the top and bottom
If the initial velocity is zero and the image is a triangle, the conclusion still holds

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1. The width of a river is 300 m, the velocity of the river is 3 M / s, and the speed of the boat in still water is 4 m / s The width of a river is 300 m, the velocity of the river is 3 M / s, and the speed of a small boat in still water is 4 m / s?
2. River width L = 300m, river velocity V1 = 3m / s, ship velocity V2 = 5m / s in still water If crossing the river with the shortest displacement, what is the sailing time and angle of the ship In addition, if the ship's speed is vertical, what is the combined speed of the ship's speed and water speed? Is V1 vertical to V2? What is the angle
3. The width of the river is d = 300 m, the velocity of the river is V1 = 1 m / s, the velocity of the ship in still water is V2 = 3 M / s, and the course of the ship forms a 30 degree angle with the upstream bank The width of the river is d = 300m, the velocity of the river is V1 = 1m / s, the velocity of the ship in still water is V2 = 3m / s, and the course of the ship forms a 30 degree angle with the upstream bank (2) Right across the bank (3) How can the course reach the opposite shore (4) What is the shortest way to cross the river
4. It is known that the width of the river is 300 m, the flow velocity is 1 m / s, and the velocity of the ship in still water is 3 M / s (1) Crossing the river in the shortest time; (2) crossing the river with the least displacement; (3) Reach 100m downstream of the opposite bank; (4) reach 100m upstream of the opposite bank These four conditions are used to calculate: the degree of the angle between the ship's course and the upstream opposite bank? The time to cross the river? Let v 1 be the velocity passing through the flow direction, V 2 be the velocity perpendicular to the flow direction, and t be the time to cross the river V1²+V2²=3² （V1+1)*t=100 t=300/V2. The same as (3): V1 & sup2; + V2 & sup2; = 3 & sup2; (v1-1) * t = 100, t = 300 / V2, t =? α =? Can you explain in detail, especially the three energies 3 & sup2; in V1 & sup2; + V2 & sup2; = 3 & sup2? Thank you very much for your answer, sincerely ask!
5. River width L = 300m, water velocity V1 = 3m / s, ship velocity V2 = 5m / s in still water River width L = 300m. Water velocity V1 = 3m / s. ship velocity V2 = 5m / s in still water. Find 1 to cross the river in the shortest time. Find 2 to cross the river in the shortest displacement. Find 3 to cross the river in the shortest displacement. When the bow of the ship is 37 degrees to the upstream bank, find the sailing time to reach the opposite bank
6. The width of the river is 200m, the static water speed of the ship is 5m / s, the water speed is 3m / s, the shortest time to cross the river? The shortest time for the ship to cross the river? The moving distance along the downstream when it is perpendicular to the opposite bank Seeking solution urgently
7. When the width of the river is 420m, the speed of the ship in still water is 4m / s, and the flow speed is 3m / s, the shortest time for the ship to cross the river is? The answer is 105s, hope to have a complete process
8. The width of the river is d = 300 m, the velocity of the river is V1 = 1 m / s, the velocity of the ship in still water is V2 = 3 M / s, and the course of the ship forms a 30 degree angle with the upstream bank How long does it take for it to cross the river (3) How can the course reach the opposite shore (4) How to cross the river in the shortest time, (2) 320m upstream （3）cosθ=1/3 (4) The bow is always perpendicular to the other side of the river, t = 100s
9. Width L = 300m, river velocity V1 = 3m / s, ship velocity V2 = 5m / s in still water, find: (1) what is the shortest time for the boat to cross the river? What is the course of the boat? (2) what is the shortest displacement for the boat to cross the river? What is the time for the boat to cross the river?
10. The car starts to move in a straight line at a constant acceleration of a = 1m / S & sup2; from a standstill, and the people at a distance of 25m behind the car chase the car at a constant speed of V = 6m / s, Can catch up with you? We need to calculate the process
11. For an object moving in a straight line with uniform acceleration, if the initial velocity V0 is 2.0 M / s, and the displacement it passes through in the third second is 4.5 m, then its acceleration is 0______ ．
12. The aircraft takes off along the horizontal runway at an acceleration of 10m / s from standstill. What is the initial speed in the third second? What is the displacement in the third second? What is the average speed in the third second? What is the average speed in the first three seconds?
13. After landing, the plane moves in a straight line with a constant deceleration at an acceleration of 6m / S2. If the landing speed is 60m / s, the distance of the plane taxiing 12s after landing is () A. 288 mB. 300 mC. 450 mD. 400 m
14. For a two digit number, the number on the one digit is 1 times larger than the number on the ten digit number; if the number on the ten digit number is exchanged with the number on the one digit number, the new number is 45 times larger than the original number, then the original two digit number is 1______ ．
15. If the rectangular wooden frame nailed by four pieces of wood is deformed into the shape of parallelogram ABCD and its area is half of the rectangular area, then the minimum inner angle of the parallelogram is () A. 30B. 45C. 60D. 90
16. The charging standards of taxis in a city are as follows: The charging standards of taxis in a city are as follows: Mileage charge RMB 5.00 for 2km and below More than 2 km, 1.80 yuan for every 1 km one way More than 2 km, 1.40 yuan for each additional kilometer Xiaoming's home is about 5 kilometers away from the school. How much does it cost to take a taxi when he comes home from school?
17. As shown in the figure, in trapezoidal ABCD, ad is parallel to BC, e is the midpoint of edge CD, and the extension line of AE and BC intersects at point F to judge the relationship between s △ ABF and s trapezoidal ABCD
18. It takes three minutes for the train to pass the 2400 meter bridge, and one minute for it to pass by the pole at the same speed. The train travels several thousand meters per minute Answer 1: This train travels x kilometers per minute, so the length of the train is x * 1 = X (x+2400)=3*x X = 1200 m / min Answer 2: I know it takes 3 minutes for the train to pass the 2400 meter bridge! Find out the speed of the train That is v = s / T = 2400m / (3 * 60) = 13.333m/s It took one minute to pass by the pole at the same speed That means the speed is the same! Vspeed = 13.333m/s t=60s S=Vt=13.333M/S *60S=799.98m=0.79998km Everybody, that's right If it's the first one, what does that one mean? Please elaborate!
19. The circumference of a rectangle is 48 decimeters. If its length and width are increased by 8 decimeters, its area will increase?
20. In the past, it took 8 hours for the toy factory to produce 1200 dolls. After the technical reform, it took only 6 hours, and the working time was shortened by several percent