Question

Analytical and graphical method of proof equations of motion

Answer 1

Analytical method to derive 1st eq. of motion:

Suppose a body is moving with an initial velocity (u) with an uniform acceleration (a) for time (t).

Now, we know,
Acceleration= rate of change in velocity/ time
Or, acceleration= initial velocity - final velocity/ time
or, a = v - u / t
or, v - u = at
or, v = u + at [1st eq. of motion]

Analytical method to derive 2nd eq. of motion:

Suppose, a body is traveling with a initial velocity (u) with an uniform acceleration (a) for time (t).
Here, to derive 2nd eq. of motion, we require the formula of average velocity.

We know, average velocity =
initial velocity + final velocity / 2 × t
Therefore, av. velocity = u + v / 2 × t ....... (i)

We know, from the 1st eq. of motion ,
v = u + at

Therefore, putting the value of v in eq. (i)

s = u + u + at / 2 × t (s = distance)

s = 2u + at /2 × t
s = (2u/2 + at/2 ) × t
s = (u + 1/2 at) × t
s = ut + 1/2at sq. [2nd eq. of motion]

Deriving 3rd eq. of motion

We know, from the 1st eq. of motion ,
v = u + at

Therefore, squaring both sides,
v sq. = ( u + at) sq.
v sq. = u sq. + 2uat + a sq. t sq.
v sq. = u sq. + 2a ( ut + 1/2at sq.)
v sq. = u sq. + 2as [3rd eq. of motion]

Note : Please note that 2 (square) should be written on top of the digits not sq. It was for my convenience.

Answer 2

Answer:

Explanation:Analytical method to derive 1st eq. of motion:

Suppose a body is moving with an initial velocity (u) with an uniform acceleration (a) for time (t).

Now, we know,

Acceleration= rate of change in velocity/ time

Or, acceleration= initial velocity - final velocity/ time

or, a = v - u / t

or, v - u = at

or, v = u + at [1st eq. of motion]

Analytical method to derive 2nd eq. of motion:

Suppose, a body is traveling with a initial velocity (u) with an uniform acceleration (a) for time (t).

Here, to derive 2nd eq. of motion, we require the formula of average velocity.

We know, average velocity =

initial velocity + final velocity / 2 × t

Therefore, av. velocity = u + v / 2 × t ....... (i)

We know, from the 1st eq. of motion ,

v = u + at

Therefore, putting the value of v in eq. (i)

s = u + u + at / 2 × t (s = distance)

s = 2u + at /2 × t

s = (2u/2 + at/2 ) × t

s = (u + 1/2 at) × t

s = ut + 1/2at sq. [2nd eq. of motion]

Deriving 3rd eq. of motion

We know, from the 1st eq. of motion ,

v = u + at

Therefore, squaring both sides,

v sq. = ( u + at) sq.

v sq. = u sq. + 2uat + a sq. t sq.

v sq. = u sq. + 2a ( ut + 1/2at sq.)

v sq. = u sq. + 2as [3rd eq. of motion]

Note : Please note that 2 (square) should be written on top of the digits not sq. It was for my convenience.