Question

derive the equations of motion in two different method.

( don't answer only one method nd also don't answer if u don't know it)​

Answer 1

Answer:

constant acceleration

For the sake of accuracy, this section should be entitled "One dimensional equations of motion for constant acceleration". Given that such a title would be a stylistic nightmare, let me begin this section with the following qualification. These equations of motion are valid only when acceleration is constant and motion is constrained to a straight line.

Given that we live in a three dimensional universe in which the only constant is change, you may be tempted to dismiss this section outright. It would be correct to say that no object has ever traveled in a straight line with a constant acceleration anywhere in the universe at any time — not today, not yesterday, not tomorrow, not five billion years ago, not thirty billion years in the future, never. This I can say with absolute metaphysical certainty.

So what good is this section then? Well, in many instances, it is useful to assume that an object did or will travel along a path that is essentially straight and with an acceleration that is nearly constant; that is, any deviation from the ideal motion can be essentially ignored. Motion along a curved path may be considered effectively one-dimensional if there is only one degree of freedom for the objects involved. A road might twist and turn and explore all sorts of directions, but the cars driving on it have only one degree of freedom — the freedom to drive in one direction or the opposite direction. (You can't drive diagonally on a road and hope to stay on it for long.) In this regard, it is not unlike motion restricted to a straight line. Approximating real situations with models based on ideal situations is not considered cheating. This is the way things get done in physics. It is such a useful technique that we will use it over and over again.

Explanation:

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Answer 2

Derivation of forest equation of motion

the first equation of motion is

v= u + at

Derivation of first equation of motion by algebraic method

It is known that the acceleration (a) of the body is defined as the rate of change of velocity

so,the acceleration can be written nas:

a = v - ut

from nthis regarding the terms , the first equation of motion is obtained which is :

v = ut + at

Derivation of first equation not motion by graphical method

consider the diagram of the velocity - time graph of a body

Derivation of a equation of motion

v= at + u

Derivation of first equation of motion by calculas method it is known that

Derivation of a equation of motion

so,

Derivation of equation of motion

Derivation of second equation of motion

The second equation of motion by algebraic method

Derivation of second equation of motion

Derivation of second equation of motion by graphical method

Taking the same diagram used in first law derivation :

Derivation of an equation of motion

In this diagram the distance travelled (s) = area of a figure

OABC = Area of rectangle OAOC + Area of triangle ABCD

Now , the area of the rectangle OADC = ut

Now the area of reactangle OADC = OA × OC = ut

And ,Area of triangle ABCD = ( 1/2)× Area of reactangle AEBD = (1/2) at 2 (since ,AD = and BD = at)

Thus, the total distance covered will be :

s= ut + (1/2) at 2

Derivation of second equation of motion by calcus method

Velocity is the rate of change of displacement

Mathematics this is expressed as

v = dsdt

Rearranging the equation we get ds = vdt

substituting the first equation not motion in the above equation , we get

ds = ( u + at) = ( udt + atdt ) ................... see in photo this