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For any arbitrary motion in space, which...

For any arbitrary motion in space, which of the following relations are true?
a) `v_("average") = (1//2)(v(t_(1) + v(t_(2))`
b) `v_("average") = [r(t_(2))-r(t_(1)]/(t_(2)-t_(1)`
`v(t) = v(0) + at`
d) `a_("average") = [v(t_(2))-v(t_(1))/[t_(2)-t_(1))`
The average stands for average of the quantity over time interval `t_(1)` to t_(2)`

A

`vecv_("average") = (1)/(2) [vecv(t_(1)) + vecv(t_(2))]`

B

`vecv_("average") = (vecr(t_(2))-vecr(t_(1)))/(t_(2)-t_(1))`

C

`vecv(t) = vecv(0) + veca t`

D

`vecr(t) = vecr(0) + vecv(0)t + (1)/(2)vecat^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
The relation (b) is true, others are false because relations (a), (c ) and (d) hold only for uniformly
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