Advice 1: How to find a private speed boat

The solution of problems on motion on the water" for many is difficult. In them there are several types of speeds, so decisive start to get confused. To learn how to solve problems of this type, it is necessary to know the definition and formula. The ability to make the scheme facilitates the understanding of the problem and contributes to the correct preparation of the equation. A correctly written equation is the most important thing in solving any type of task. Instruction
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In the movement on the river" present speed: the speed (V) speed current (Vпо tech.), speed against the current (V [PR]. tech.), flow rate (Vтеч.). It should be noted that private speed boats is the speed in still water. To find the speed of the flow, it is necessary for the flow rate to add your own. To find the speed against the current, it is necessary from own rate, subtract the rate of flow.
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The first thing you need to learn and know "by heart" formula. Record and remember:

Vпо tech=VC+Vтеч.

V [PR]. tech.=VC-Vтеч.

V [PR]. tech=tech Vпо. - 2Vтеч.

Vпо tech.=V [PR]. tech+2Vтеч.

Vтеч.=(Vпо tech. - V [PR]. tech)/2

VC=(Vпо tech.+V [PR] tech.)/2 or VC=Vпо tech.+Vтеч.
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For example, let us consider how to find their own speed and to solve problems of this type.

Example 1.The speed of the boat upstream 21.8 km/h and upstream 17.2 km/h to Find a private speed boat and speed of river flow.

Solution: According to the formula: VC=(Vпо tech.+V [PR] tech.)/2 and Vтеч.=(Vпо tech. - V [PR]. tech)/2, we find:

Vтеч = (21,8 - 17,2)/2=4,6\2=2,3 (km/h)

VC = V [PR] tech.+Vтеч=17,2+2,3=19,5 (km/h)

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Example 2. The steamer passed upstream 24 miles and back, spending the trip back to 20 minutes less than when moving against the current. Find his own speed in still water if the speed of the current is 3 km/h.

For X take a private speed boat. Set up a table where you put all the data.

Against tech. The flow

Distance 24 24

Speed X-3 X+3

time 24/ (X-3) 24/ (X+3)

Knowing that on the way back the boat spent 20 minutes less time than on the path, we compose and solve the equation.

20 min=1/3 hours.

24/ (X-3) – 24/ (X+3) = 1/3

24*3(X+3) – (24*3(X-3)) – ((X-3)(X+3))=0

72+216-72+216-x2+9=0

441-x2=0

X2=441

X=21(km/h) – private speed boat.

Note
The speed of the raft is considered to be equal to the speed of the water.

Advice 2 : How to calculate speed

Modern life is in constant motion: cars, trains, airplanes, all in a hurry, running somewhere, and often it is important to calculate the speed of this movement. To calculate the rate is the formula V=S/t where V is velocity, S – distance, t – time. Let's consider an example to understand the algorithm of actions. Instruction
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Interesting to know, how fast do you go? Select the track, footage of which you know (in the stadium, for example). Note the time and go at your own pace. So, if the path length of 500 meters (0.5 km) and you held it for 5 minutes, then divide 500 by 5. It turns out that your velocity is 100 m/min.

If the bike you rode her for 3 minutes, then your speed is 167 m/min.

On the machine for 1 minute, then the speed of 500 m/min. 2
To convert the speed from m/min to m/sec, divide the speed in m/min by 60 (number seconds in a minute).

So, it turns out that when walking your speed 100 m/min / 60 = 1,67 m/sec.

Bike: 167 m/min / 60 = 2.78 m/sec.

Machine: 500 m/min / 60 = 8.33 and m/s. 3
To translate velocity from m/sec into km/h speed in km/h divide by 1000 (number of meters in 1 kilometer) and the resulting number multiply by 3600 (number of seconds in 1 hour).

Thus, it appears that walking speed is 1.67 m/s / 1000*3600 = 6 km/h.

Bike: 2.78 m/sec / 1000*3600 = 10 km/h.

Machine: 8,33 m/s / 1000*3600 = 30 km/h.
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To simplify the transfer speed from m/sec into km/h use a factor of 3.6, which is applied as follows: speed in m/s*3,6=speed in km/h.

Walking: 1,67 m/s*3,6 = 6 km/h.

Bike: 2.78 m/s*3,6 = 10 km/h.

Machine: 8,33 m/s*3,6= 30 km/h.

Obviously, it's much easier to remember the ratio is 3.6, than the whole procedure of multiplication is division. In this case, you will easily translate the speed from one value to another. Advice 3 : How to find time knowing the distance and speed

The concept of speed, time and distance known each other since middle school. But you must understand that they are much wider than the base of the national curriculum. And in order to use the same formula we have to take into account a number of conditions. Instruction
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Given the assumptions of classical mechanics, the velocity characterizes the speed of movement of a point in space. This is a vector quantity, i.e., velocity has a direction. The speed is usually measured in kilometers per hour or in metres per second (symbol km/h and m/s respectively).
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Time in classical mechanics are continuous, nothing is defined. For measurement uses a periodic sequence of events, which is considered the benchmark of the minimum period of time. This principle is familiar to everyone for example, ordinary hours. To solve elementary physics problems time represent seconds (), minutes (m) or hours (h).
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Distance is a key concept in many Sciences. In a General sense it can be defined as the degree of remoteness of the objects. Problems in school physics, distance is usually measured in centimeters (cm) meters (m) kilometers (km), etc.
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We must distinguish between two concepts: the distance between the objects and the path that passes the point, overcoming this distance. After all, when you move a point can move along the shortest distance between points and can, for example, to go on a zigzag path. The distance between the points remains the same, but the way she's going to do much more.
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Vary accordingly, the average travel speed and average speed path. For example, horses, running round a racetrack, the average speed of the path different from zero. While the moving speed is equal to zero, since the horse returned to the same point from which started the movement.
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That is the average speed of the path is equal to the ratio of the traversed point the way to the time for which the path was traversed. To remember this ratio just. Traditionally, the distance indicated by the letter s (from the Latin spatium "space"), velocity – v (eng. velocity), and time – t (eng. time). Draw a triangle in the upper part of which distance, in base – time and speed (see figure). Now close the desired value (e.g., time). It turns out that the time equal to the remaining fraction – the ratio of the distance to speed.
Carefully watch the units of measurement of variables. If a task speed is defined in meters per second, and the distance in kilometers will have to either switch the speed in km/h or distance in meters.

Advice 4 : How to calculate driving time

Often people want to know how long it will take to move from one place to another. It can be a trip in another part of town and to another country. We will understand how to do it. You will need
• card;
• - GPS Navigator.
Instruction
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Before you can calculate the time of motion, determine the distance to the destination using the program Google Earth (Google maps). Using the ruler tool get directions, - get exact distance to the end point. This value is denoted by the letter s. In addition to GoogleMaps distance can be calculated by the map or the directory of roads.
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Find out the average moving speed V. This value depends on how you plan to move. For example, the average speed of the car in the city - 40-60 km/h, outside town - 90 to 120 km/h If you walk, take the speed is 4-6 mph, or about 1.5 m/s.
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When the path and speed is found, you can start calculating the time of movement. To do this, use the formula: t=s/v, where t is the desired time, and s and v - values found above.
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It should be noted that before the division the dimension of the values necessary to result in the same measurement units. If the path you have in metres, then take the speed in meters per second. Conversely, if you know the path in kilometers, and speed take the kilometers per hour. In the first case, get the time in seconds and the second in hours. For example, find the time of motion, if you know the distance between the homes of two friends: s=2500 meters, while the car rides from one home to another through the lanes at speed v=36 km/h. To start, bring the speed in m/s: 36/3,6 = 10 m/s. the calculations according to the formula: t = s/v = 2500/10 = 250 seconds. As you can see, the journey time is slightly longer than 4 minutes.
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As you can see, this method is rather complicated, and its accuracy is not very high, because the speed is taken "by eye". But if you have a GPS Navigator (as a separate device or built-in feature in the phone), it is possible to significantly improve the accuracy of the calculations.
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Take a GPS device, set the map route. The program will immediately plot a route and display it on the map, denoting distance. Start to move on the route – on foot or by transport. Navigator will analyze the speed of your movement and automatically calculate the planned time path. At the end of your journey, navigate to aggregate information and view the exact time you spent on the movement.
To determine the time of movement, use a web calculator offered by many transport websites.

Advice 5 : How to find the time, knowing the speed

Tasks on kinematics, which is necessary to calculate speed, time or path of a uniformly and rectilinearly moving bodies, meet in the school course of algebra and physics. For their solution find it in the condition values, which can be interconnected to equalize. If the condition is required to determine the time at a known speed, use the following instructions. You will need
• - handle;
• paper for records.
Instruction
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The simplest case is the motion of a body with a given uniform velocityu. Know the distance that the body has passed. Find time in transit: t = S/v, h, where S is distance, v is the average velocity of the body.
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The second example is for a counter motion. From point A to point b the car is moving with speedu 50 km/h. to Meet him from point B at the same time I left the moped with the speedu 30 km/h. The distance between the points A and b 100 km is Required to find the timethrough which they will meet. 3
Designate a meeting point with the letter K. Let the distance of AK, who drove the car be x km. Then the path of the rider will amount to 100's of km. From the problem statement it follows that the time in the way of car and motorbike alike. Write down the equation: x/v = (S-x)/v’, where v, v’ – vehicle speed, and a moped. Substituting the data solve the equation: x = 62,5 km. Now find the time: t = for 62.5/50 = 1.25 hours or 1 hour and 15 minutes.
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The third example – given the same conditions, but left 20 minutes late the bike. To determine how much time will the car before meeting with a moped.
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Write down the equation, similar to the previous one. But in this case time of a moped in the path will be 20 minutes more than the car. For the adjustment of the parts, subtract one-third of the hours from the right side of the expression: x/v = (S-x)/v’-1/3. Find the x – 56,25. Calculate time: t = 56,25/50 = 1,125 hours, or 1 hour 7 minutes 30 seconds.
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The fourth example is a challenge for a body moving in one direction. Car and moped with the same speed move from point A. it is Known that the car left half an hour later. After a time he will catch up with the moped? 7
In this case, the same will be the distance traveled of the vehicle. Let time in the path of the car be x hours then time in the path of the moped will be x+0,5 hours. You got the equation: vx = v’(x+0,5). Solve the equation, substituting the value of speed, and find x – 0.75 hour or 45 minutes.
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The fifth example is a car and a moped with the same speed moving in the same direction, but the moped went from point b, located at a distance of 10 km from point A, half an hour earlier. To calculate, through what time after the start of the car will overtake the moped. 9
The distance that the car drove 10 km more. Add this difference to the path of the motorcycle and align the parts of the expression: vx = v’(x+0,5)-10. Substituting the values of speed and solved it, you will get the answer: t = 1.25 hours or 1 hour and 15 minutes.
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