Instruction
1
When solving problems in the movement the main parameters are:
the path, indicated generally as S,
the speed – V and
time - t.
The dependence between these parameters is expressed by the following formulas:
S=Vt, V=S/t and t=S/V
To avoid confusion in units of measurement, these parameters must be specified in one system. For example, if the time is measured in hours and the distance traveled in kilometers, the speed, respectively, must be measured in kilometer/hour.
When solving problems of this type are usually produced by the following steps:
1. Select one of the unknown parameters and is denoted by the letter x (y, z, etc.)
2. Specify which of the three basic parameters are known.
3. A third of the remaining parameters using the above formulae is expressed through the other two.
4. Based on the conditions of the problem, make an equation that links an unknown value with known parameters.
5. Solve the resulting equation.
6. Check the found roots of the equation under tasks.
In some cases, solve the problem by means of the drawing (regardless of the quality of the picture).
the path, indicated generally as S,
the speed – V and
time - t.
The dependence between these parameters is expressed by the following formulas:
S=Vt, V=S/t and t=S/V
To avoid confusion in units of measurement, these parameters must be specified in one system. For example, if the time is measured in hours and the distance traveled in kilometers, the speed, respectively, must be measured in kilometer/hour.
When solving problems of this type are usually produced by the following steps:
1. Select one of the unknown parameters and is denoted by the letter x (y, z, etc.)
2. Specify which of the three basic parameters are known.
3. A third of the remaining parameters using the above formulae is expressed through the other two.
4. Based on the conditions of the problem, make an equation that links an unknown value with known parameters.
5. Solve the resulting equation.
6. Check the found roots of the equation under tasks.
In some cases, solve the problem by means of the drawing (regardless of the quality of the picture).
2
Example 1.
To solve the problem:
Skier passing 5 km in the same amount of time for which the pedestrian manages to pass 2 km.
To find this time, if it is known that the speed of the skier more the walking speed of 6 km/h. Determine the speed of the pedestrian and skier.
Let us denote the desired time (in hours) using t.
Then, by the formula V=S/t, the speed of the skier equal to 5/t km/h and walking speed is equal to 2/t km/h.
Using conditions the task can write the equation:
5/t – 2/t = 6
Where is defined as: t=0.5
Therefore: speed of a pedestrian is 4 km/h, and skier - 10 km/h.
Response: 0.5 hours; 4 km/h; 10 km/h.
To solve the problem:
Skier passing 5 km in the same amount of time for which the pedestrian manages to pass 2 km.
To find this time, if it is known that the speed of the skier more the walking speed of 6 km/h. Determine the speed of the pedestrian and skier.
Let us denote the desired time (in hours) using t.
Then, by the formula V=S/t, the speed of the skier equal to 5/t km/h and walking speed is equal to 2/t km/h.
Using conditions the task can write the equation:
5/t – 2/t = 6
Where is defined as: t=0.5
Therefore: speed of a pedestrian is 4 km/h, and skier - 10 km/h.
Response: 0.5 hours; 4 km/h; 10 km/h.
3
Example 2.
Solve the above problem in a different way:
Denote the walking speed using V (km/h).
Then the velocity of the skier will be (V+6) km/h.
In accordance with the formula: t=S/V, the time can be determined according to the following expression:
t=5/(V+6)=2/V
How elementary is:
V=4,
t=0.5.
Solve the above problem in a different way:
Denote the walking speed using V (km/h).
Then the velocity of the skier will be (V+6) km/h.
In accordance with the formula: t=S/V, the time can be determined according to the following expression:
t=5/(V+6)=2/V
How elementary is:
V=4,
t=0.5.
