During an accelerated motion of a particle,what is the relation between the average velocity and the final velocity?

Dear student,

• Motion with constant acceleration or uniformly accelerated motion is that in which velocity changes at the same rate troughout motion.
• When the acceleration of the moving object is constant its average acceleration and instantaneous acceleration are equal. Thus we have

  aavg= a =	v2-v1
  	t2-t1

                                                                                     
• Let v₀ be the velocity at initial time t=0 and v be the velocity of object at some other instant of time say at t₂=t then above eq. 7 becomes

  a =	v-v0
  	t-0

  or , v=v₀+at                        
• Graphically this relation is represented as
  
  
• In the same way average velocity can be written as

  vavg =	x-x0
  	t-0

  where x₀ is the position of object at time t=0 and v_avg is the averag velocity between time t=0 to time t.The above equation then gives
  x=x₀+v_avgt                  
  but for the interval t=0 to t the average velocity is

  vavg =	v0+v
  	2

                                                           
  Now from eq. 8 we find
  v_avg = v₀ + ½(at)                  
  putting this in eq. 9 we find
  x = x₀ + v₀t + ½(at²)
  or,
• x - x₀ = v₀t + ½(at²)

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi         

for constant accleration(a) ....

let initial velocity is u & final velocity  is v then

v² = u² + 2aS ...........1                  (S is displacement)

average velocity = total distlacement /total time = S/t       ................2

v = u+at

t = v-u/a      ..............3

V_avg = Sa/(v-u)          ............4

from eq 4 & 1 eliminating S

V_avg = v²-u²/2(v-u)

 V_avg = (v+u)/2

this is the required relation

in a uniformly accelarated motion it is

v = final velocity

a = accelaration

u = initial velocity

t = time taken

s = distance travelled

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so the relation is

v = u + at ------------------------(i)

2*a*s = v² - u²           ----------------------- (ii)

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Please approve