Question

For any arbitrary motion in space, which of the following relations is true? (The average stands for average of the quantity over the time interval $t_1$ to $t_2$)

• A. $\vec{v}_{average}=\frac{1}{2}\left[\vec{v}\left(t_{1}\right)+\vec{v}\left(t_{2}\right)\right]$
• B. $\vec{v}_{average}=\frac{\vec{r}\left(t_{2}\right)-\vec{r}\left(t_{1}\right)}{t_{2}-t_{1}}$
• C. $\vec{v}\left(t\right)=\vec{v}\left(0\right)+\vec{a}t$
• D. $\vec{r}\left(t\right)=\vec{r}\left(0\right)+\vec{v}\left(0\right)t+\frac{1}{2}\vec{a}t^{2}$

Answer 1

Answer: (B)

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

Answer 2

The relation (b) is true, others are false because relations (a), (c) and (d) hold only for uniformly accelerated motion.