Equation of motion, physics notes

EQUATIONS OF MOTION EQUATIONS OF MOTION

     

FIRST EQUATION OF MOTION V_f = V_i + at

  Consider a body initial moving with velocity "Vi". After certain interval of time "t", its velocity becomes "V_f". Now

Change in velocity = V_f - V_i OR DV =V_f – V_i

Due to change in velocity, an acceleration "a" is produced in the body. Acceleration is given by

a = DV/t

  Putting the value of "DV"

a = (Vf – Vi)/t at = V_f – V_i at + V_i =V_f OR

SECOND EQUATION OF MOTION OR S = Vit + 1/2at²

  Consider a car moving on a straight road with an initial velocity equal to ‘V_i’. After an interval of time ‘t’ its velocity becomes ‘V_f’. Now first we will determine the average velocity of body.

Average velocity = (Initial velocity + final velocity)/2 OR V_av = (V_i + V_f)/2

but V_f = V_i + at Putting the value of Vf

V_av = (V_i + V_i + at)/2 V_av = (2V_i + at)/2   V_av = 2V_i/2 + at/2  Vav = V_i + at/2                           V_av = V_i + 1/2at.......................................(i)

we know that

S = V_av x t

Putting the value of ‘V_av’

S = [V_i + 1/2at] t

THIRD EQUATION OF MOTION (2aS = V_f² – V_i²⁾

  Initial velocity, final velocity, acceleration, and distance are related in third equation of motion. Suppose a body moving initially with velocity ‘V_i’. After certain interval of time its velocity becomes ‘V_f’. Due to change in velocity, acceleration ‘a’ is produced in the body. Let the body travels a distance of ‘s’ meters. According to first equation of motion:

V_f = V_i + at      OR V_f – V_i = at OR                          (V_f – V_i)/a = t....................(i)

Average velocity of body is given by:

V_av = (Initial velocity + Final velocity)/2                               V_av = (V_i + V_f)/2.................. (ii)

we know that :

              S = V_av x t.................. (ii)

Putting the value of V_av and t from equation (i) and (ii) in equation (iii)

S = { (V_f + V_i)/2} { (V_f – V_i)/a} 2aS = (V_f + V_i)(V_f – V_i)

According to [ (a+b)(a-b)=a²-b^2]