Uniform speed straight line

basic formula

Speed ​​Time Formula :

displacement - time formula :

;

speed - displacement formula :

;

wherein a is acceleration,

is the initial speed,

to final velocity, t the time used for the process, that during the displacement s.

displacement variation - time formula:

< section>Representative adjacent time period equal to the displacement difference, the adjacent T represents the time length of a time period equal

conditions

uniform variable linear motion of the object also complies with the following two:

(1) suffered no resultant force is zero, and remains unchanged;

(2) combined force initial speed along the same line.

Category

at uniform speed linear motion, even if the speed of an object increases with time, this motion is called uniformly accelerated linear motion; if the speed of the object with time decreases uniformly this motion is called uniform deceleration linear motion.

If the direction of velocity acceleration in the same direction (i.e., the same number), it is accelerating; if the opposite (i.e. of opposite sign) to the velocity direction of the direction of acceleration is the deceleration.

law derived

a displacement equation is derived:

(1) Since the speed uniform speed linear motion is uniform changes, so the average speed = (First speed + final velocity) instantaneous speed / 2 = intermediate time

is displaced uniformly variable linear motion = average speed × time, so the

using the displacement formula

and average speed formula

, an average speed of

=

(2) using the calculus basic definition, a velocity function (with respect to time) is the derivative of the displacement function of an acceleration function is the derivative on the velocity function written as equation is

,

Thus

,

is the initial velocity, can be any constant

Further there, (p < section>in uniform speed linear motion), apparently at t = 0, s = 0, so that the arbitrary constant C = 0, so there

this is the displacement formula.

(3)

(

Representative adjacent time period equal to the displacement difference, T represents a length of time equal to the adjacent period)

One second displacement:

seconds before the displacement:

can be calculated, two seconds before the displacement of the difference

. This is derived from the initial speed zero motion, the initial velocity is not zero the same conclusions can be obtained.

(4)

simultaneous displacement of formula

and speed formula

, it can be demonstrated .

Second, the speed formula is derived

(1) intermediate the speed of displacement

Proof: By the displacement of formula

, a

x transducer available

,

to give

then

after

is substituted into the equation, we obtain

finishing square root, to obtain the

(2) intermediate speed time

prove

referred to as ★ formula,

denoted ● formula

● formula +

★ formula finishing available

the

substituting

give

proportional

(1) a significant proportion of the relationship

a

, to give

.

a

, to give

, or

.

a

, to give

, or

.

(2) a substantial proportion (initially the speed of uniformly accelerated motion 0)

① second end of the first, second end of the second, ......, n th speed second end than

is derived:

1 seconds ago ②, within the first two seconds, ... ..., displacement ratio of n seconds before the

.

is derived:

③ a first inner t, the second t, ......, the n-th T (the same time) ratio displacements

is derived:

④ the front 1x, front 2x, before 3x ......, than the time

nx before deriving the desired displacement:

, the ratio of displacement is increased when , the ratio of the root is also proportionally increased.

⑤ by the 1st s, 2nd s, third s, ......, n th s (equal to the displacement by continuous) than the time required

is derived:

typical applications

freefall

< b> a, the concept

object only by gravity falling motion from rest.

1, the kinematic characteristics: its size, direction does.

2, the mechanical characteristics: only by gravity in vacuo and the object, or in the air, the air resistance is small suffered object, and the object can be neglected compared to gravity.

3, nature of the movement: the free fall is the initial velocity of zero uniformly accelerated linear motion. Therefore, all laws and uniform linear motion transmission zero initial velocity ratio between the various uniformly accelerated linear motion can be used in free fall.

4, the acceleration of free fall: in the same place, all the objects in a free fall acceleration are the same, this is called gravitational acceleration, expressed in g, the different latitude on the earth, a different value of g. Which is a vertically downward direction. When taking 9.8

usually calculated rough calculation, taking 10

.

II Law

is zero initial velocity in free fall, g is the acceleration rate of the uniform linear motion, the movement of which follows:

1, three basic formula:

;

;

2, three special formula:

(1) in successive equal time difference within (T) is a constant displacement value, i.e.

(2) within a certain period of time intermediate First the instantaneous speed equal to the average velocity of this time, i.e.,

instantaneous speed (3) the displacement of certain intermediate position

and this displacement , terminal velocity

and

relationship is

3, four ratio equation (see the above proportional relationship)

on the vertical projectile motion

object having upward vertical initial velocity, acceleration of gravity g is always uniform transmission of motion, it can be divided into uniform deceleration at the time of dropping and throwing two of the process of free fall. It is the initial velocity

(

is not equal to 0) is uniform deceleration engagement motion linear motion and free fall, and equal movement during rise and fall two process takes time, only by gravity and a force opposite to the direction of receiving the initial velocity direction.

formula

(in

direction is the positive direction):

(1)

(2)

(3)

(4) < section>

(5) vertical parabolic time required to reach the maximum height of the

, and the condition may be speed formula

obtained, i.e.,

NOTE: may be the rising process

,

leveling speed linear motion, free fall drop phase is analyzed.