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

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

Grade:12th Pass

3 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

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 vavg is the averag velocity between time t=0 to time t.The above equation then gives
    x=x0+vavgt                  
    but for the interval t=0 to t the average velocity is
    vavg = v0+v
    2
                                                             
    Now from eq. 8 we find
    vavg = 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         

vikas askiitian expert
509 Points
10 years ago

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

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

 

from eq 4 & 1 eliminating S

Vavg = v2-u2/2(v-u)

 Vavg = (v+u)/2

 

this is the required relation

Sudheesh Singanamalla
114 Points
10 years ago

in a uniformly accelarated motion it is

v = final velocity

a = accelaration

u = initial velocity

t = time taken

s = distance travelled

----------------

so the relation is

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

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

---------------

 

Please approve

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