The movement of various bodies in the environment is characterized by a number of sizes, one of which – average speed. This generalized indicator determines body speed on all movement. Knowing dependence of the module of instantaneous velocity on time, average speed can be found by means of a graphic method.
Instruction
1. Construct according to a task the schedule of dependence of speed of the movement of a body from time of v(t). Here horizontal coordinate represents change of time (c), vertical – speeds (m/s). As a rule, in tasks the uneven moving of bodies to certain periods is considered. Any change of speed on graphics will be displayed by increase or decrease. For example, at a body start of motion with continuous acceleration during 20 about its speed as a result made 15 m/s. Postpone on graphics the straight line which is beginning at the beginning of coordinates (0, 0) and coming to an end in a point (20, 15) where 20 with are postponed on t time axis to the right, and 15 m/s – up speed. In the presence of uniform motion of a body display it a direct, parallel horizontal axis.
2. For finding of average speed of movement it is necessary to know a way and time spent for the movement. Calculate the area of S under curve v(t) which is graphical representation of the way of L passed by a body. Often the schedule of movement limits a figure a trapeze. Its area is on a formula: S = ½ * (t0 + t1) *vn, where t0 and t1 – the trapeze bases – parts of the schedule of speed, vn – the figure height, here the maximum speed in way. Substitute the known values in a formula and calculate result. If the schedule of v(t) represents not a trapeze, its area is calculated on other formulas, depending on the received figure.
3. Find the average speed of the movement of a body on a formula Vcp = L/t. Having substituted the set time of movement and the calculated way, count numerical value of average speed.
4. Average speed can be calculated also according to the schedule of dependence of a way from time of l(t). For this purpose connect a straight line initial and final points of the considered site of movement. Average speed of a body will be equal to a tangent of angle of an inclination of the received straight line to time axis.