Question

For any arbitrary motion in space, which of the following relations is true?

• A. ${\overrightarrow{v}}_{average} = \frac{1}{2}\lbrack\overrightarrow{v}(t_{1}) + \overrightarrow{v}(t_{2})\rbrack$
• B. ${\overrightarrow{v}}_{average} = \frac{\overrightarrow{r}(t_{2}) - \overrightarrow{r}(t_{1})}{t_{2} - t_{1}}$
• C. $\overrightarrow{v}(t) = \overrightarrow{v}(0) + \overrightarrow{a}t$
• D. $\overrightarrow{r}(t) = \overrightarrow{r}(0) + \overrightarrow{v}(0)t + \frac{1}{2}\overrightarrow{a}t^{2}$

Answer 1

Answer: (B)

${\overrightarrow{v}}_{average} = \frac{\overrightarrow{r}(t_{2}) - \overrightarrow{r}(t_{1})}{t_{2} - t_{1}}$

Answer 2

The relation (2) is true, other are false because relations (1), (3) and (4) hold only for uniform accelerated motions.