A particle starts from rest with constant acceleration. The ratio of space-average velocity to the time average velocity is :

Options

A. `(1)/(2)`
B. `(3)/(4)`
C. `(4)/(3)`
D. `(3)/(2)`

Answer

C

Explanation

`v=at, (ds)/(dt)=atrArrds=at dt`
`(V_("avg"))_("space")=(intVds)/(intds)=(int at at dt)/(int ad dt )=(a^(2)(t^(3))/(3))/((at^(2))/(2))=(2at)/(3)`
`(V_("avg"))_("time")=(int v dt)/(int dt)=(int at dt a (t^(2))/(2))/(int dt t)=(at)/(2)`
`((V_("avg"))_("space"))/((V_("avg"))_("time"))=((2at)/(3))/((at)/(2))=(4)/(3)`