Dimensions of position vector derivatives – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Dimensions of position vector derivatives

Assertion (A): If \(vec{r}\) is the position vector then dimensions of \(\frac{d^2vec{r}}{dt^2}\) is \([M^0L^1T^{-2}]\).
Reason (R): Dimensions of \(int \left(\frac{d^2vec{r}}{dt^2}\right) dt\) is \([M^0L^1T^{-1}]\) where \(\vec{r} \rightarrow\) position vector, \(t \rightarrow\) time.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

The second derivative of position with respect to time represents acceleration with dimensions \([L T^{-2}]\). Integrating this acceleration with respect to time yields velocity with dimensions \([L T^{-1}]\). Both statements are true, but R is not the explanation of A.

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