Physics

Physics

Problem

3.20 For any arbitrary motion in space, which of the following relations are true : (a) vaverage =(1/2)(v(t1)+v(t2))\mathbf{v}_{\text {average }}=(1 / 2)\left(\mathbf{v}\left(t_{1}\right)+\mathbf{v}\left(t_{2}\right)\right) (b) vaverage =[r(t2)−r(t1)]/(t2−t1)\mathbf{v}_{\text {average }}=\left[\mathbf{r}\left(t_{2}\right)-\mathbf{r}\left(t_{1}\right)\right]/\left(t_{2}-t_{1}\right) (c) v(t)=v(0)+at\mathbf{v}(t)=\mathbf{v}(0)+\mathbf{a} t (d) r(t)=r(0)+v(0)t+(1/2)at2\mathbf{r}(t)=\mathbf{r}(0)+\mathbf{v}(0) t+(1 / 2) \mathbf{a} t^{2} (e) aaverage =[v(t2)−v(t1)]/(t2−t1)\mathbf{a}_{\text {average }}=\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 t1t_{1} to t2t_{2} ) (a) vaverage =(1/2)(v(t1)+v(t2))\mathbf{v}_{\text {average }}=(1 / 2)\left(\mathbf{v}\left(t_{1}\right)+\mathbf{v}\left(t_{2}\right)\right) (b) vaverage =[r(t2)−r(t1)]/(t2−t1)\mathbf{v}_{\text {average }}=\left[\mathbf{r}\left(t_{2}\right)-\mathbf{r}\left(t_{1}\right)\right]/\left(t_{2}-t_{1}\right) (c) v(t)=v(0)+at\mathbf{v}(t)=\mathbf{v}(0)+\mathbf{a} t (d) r(t)=r(0)+v(0)t+(1/2)at2\mathbf{r}(t)=\mathbf{r}(0)+\mathbf{v}(0) t+(1 / 2) \mathbf{a} t^{2} (e) aaverage =[v(t2)−v(t1)]/(t2−t1)\mathbf{a}_{\text {average }}=\left[\mathbf{v}\left(t_{2}\right)-\mathbf{v}\left(t_{1}\right)\right]/\left(t_{2}-t_{1}\right)

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