In the simplest tasks on the speed and distance you need to use common sense.For example, if it is said that the cyclist rode 30 minutes at a speed of 15 kilometers per hour, it is evident that their path is traversed by 0.5 h • 15km / h = 7.5 km.Hours are reduced, remain kilometers.In order to understand the ongoing process is useful to record the value of their dimensions.
If the object in question is moving unevenly, it takes the laws of mechanics.Suppose, for example, a cyclist while moving gradually tired, so for every 3 minutes of its rate decreased by 1 km / h.This indicates the presence of negative acceleration equal modulo a = 1km / 0,05ch² or deceleration of 20 kilometers an hour in the square.The equation for
distance traveled then takes the form L = v0 • t-at² / 2, where t - time way.Slow down, the cyclist will stop.For half an hour will pass the cyclist is not 7.5, and only 5 kilometers.
can find the total time path if the path to take for the point of the beginning of the movement to a halt.To do this, create a rate equation which is linear as a cyclist slowed down evenly: v = v0-at.Thus, at the end of the path v = 0, the initial velocity of v0 = 15, a = acceleration module 20, so 15-20t = 0.Hence it is easy to express t: 20t = 15, t = 3/4 and t = 0,75.Thus, if the transfer results in minutes, the cyclist will ride to the bus stop 45 minutes, after which it is likely to sit relax and have a snack.
from found time can determine the distance that was able to overcome a tourist.To do this, t = 0,75 should be substituted into the formula L = v0 • t-at² / 2, while L = 15 • 0,75-20 • 0,75² / 2, L = 5,625 (km).It is easy to notice that the cyclist to slow down unprofitable, is not it possible to be late everywhere.
speed of the body can be set arbitrarily according to the equation of time, even such exotic as v = arcsin (t) -3t².In general, to find the distance from this, it is necessary to integrate the speed formula.When integrating appears constant, which must be found from the initial conditions (or any other fixed conditions known in the problem).