एक नियत त्वरण से चलने वाले कण के समयान्तरालों `t_(1),t_(2)` व `t_(3)` पर औसत वेग, क्रमशः `v_(1),v_(2)` व `v_(3)` हैं। निम्नलिखित में से कौन-सा सम्बन्ध सही है?

Options

A. `(v_(1)-v_(2))/(v_(2)-v_(3))=(t_(1)-t_(2))/(t_(2)+t_(3))`
B. `(v_(1)-v_(2))/(v_(2)-v_(3))=(t_(1)+t_(2))/(t_(1)-t_(2))`
C. `(v_(1)-v_(2))/(v_(2)-v_(3))=(t_(1)-t_(2))/(t_(2)-t_(3))`
D. `(v_(1)-v_(2))/(v_(2)-v_(3))=(t_(1)+t_(2))/(t_(2)+t_(3))`

Answer

D

Explanation

`v_(1)=(u+v._(1))/(2)=(u+u+at_(1))/(2)=u+(1)/(2)at_(1)`
`v_(2)=(v._(1)+v._(2))/(2)=((u+at_(1))+u+a(t_(1)+t_(2)))/(2)`
`=u+at_(1)+(1)/(2)at_(2)`
`v_(3)=(v._(2)+v._(3))/(2)=((u+at_(1)+at_(2))+u+a(t_(1)+t_(2)+t_(3)))/(2)`
`=u+at_(1)+at_(2)+(1)/(2)at_(3)`
तब `v_(1)-v_(2)=-(1)/(2)a(t_(1)+t_(2))`
`v_(2)-v_(3)=-(1)/(2)a(t_(2)-t_(3))`
`:.(v_(1)-v_(2))/(v_(2)-v_(3))=(t_(1)+t_(2))/(t_(2)+t_(3))`