For any arbitrary motion in space, which of the following relations are true:

Question.
For any arbitrary motion in space, which of the following relations are true:

(a) $\mathbf{v}_{\text {aventes }}=\left(\frac{1}{2}\right)\left(\mathbf{v}\left(t_{1}\right)+\mathbf{v}\left(t_{2}\right)\right)$

(b) $\mathbf{v}_{\text {avenee }}=\frac{\left[\mathbf{r}\left(t_{2}\right)-\mathbf{r}\left(t_{1}\right)\right]}{\left(t_{2}-t_{1}\right)}$

(c) $\mathbf{v}(t)=\mathbf{v}(0)+\mathbf{a} t$

(d) $\mathbf{r}(t)=\mathbf{r}(0)+\mathbf{v}(0) t+\left(\frac{1}{2}\right) \mathbf{a} t^{2}$

(e) $\mathbf{a}_{\text {averace }}=\frac{\left[\mathbf{v}\left(t_{2}\right)-\mathbf{v}\left(t_{1}\right)\right]}{\left(t_{2}-t_{1}\right)}$

(The 'average' stands for average of the quantity over the time interval $t_{1}$ to $t_{2}$ )