The distance which will pass a body during the movement directly depends on its speed: the is higher the speed, the bigger distance the body will be able to cover. And speed can depend on acceleration which, in turn, is defined by force operating on a body.
Instruction
1. In the simplest tasks on the speed and distance it is necessary to be guided by common sense. For example, if it is told that the cyclist went 30 minutes with a speed of 15 kilometers per hour, then it is obvious that the way passed by him is equal to 0.5 h·15km / h =7.5 km. Hours are reduced, there are kilometers. For understanding of an essence of the happening process it is useful to write down sizes with their dimensions.
2. If the considered object moves unevenly, laws of mechanics go into action. Let, for example, the cyclist in the direction of travel gradually was tired so in each 3 minutes his speed decreased by 1 km/h. It says about existence of the negative acceleration equal on the module a=1km/0.05ch², or delays in 20 kilometers for an hour in a square. The equation for the passable way then will take L=v0 form • t-at²/2 where t is time of a way. Slowing down, the cyclist will stop. For half an hour the cyclist will pass any more not 7.5 but only 5 kilometers.
3. It is possible to find the general time of a way if to take a point from a start of motion to a full stop for a way. For this purpose it is necessary to work out the speed equation which will be linear as the cyclist slowed down evenly: v=v0-at. So, at the end of the way of v=0, the initial speed of v0=15, the module of acceleration a=20, therefore 15-20t=0. From here it is easy to express t: 20t=15, t=3/4 or t=0.75. Thus, if to translate result in minutes, the cyclist will go to a stop of 45 minutes then he will probably sit down to have a rest and bite.
4. From the found time it is possible to define distance which the tourist managed to overcome. For this t=0.75 it is necessary to substitute in formula L=v0 • t-at²/2, then L=15•0.75-20•0.75²/2, L=5.625 (km). It is easy to notice that it is unprofitable to slow down to the cyclist, it is so possible to be late everywhere.
5. Speed of the movement of a body can be set by any equation of dependence on time, even such exotic as v=arcsin(t)-3t². Generally, to find from this distance, it is necessary to integrate a formula of speed. At integration there will be a constant which should be found from entry conditions (or from any other fixed conditions known in a task).