Problem 7.10 Challenge

a) จาก \(Δ\vec{r} = \vec{r}(4) - \vec{r}(0)\)

îĵk̂îĵk̂

\(\Delta \vec{r} = (4(4)^{2} + 5(4) + 6 ) - (4(0)^{2} + 5(0) + 6 )\)

îĵ

\(\Delta \vec{r} = 64.0 + 20.0 m \;\blacksquare\)

b) จาก \(\vec{v}_{av}=\frac{\Delta \vec{r}}{\Delta t}\)

îĵ

\(\vec{v}_{av}= 16.0 + 5.00 m/s \;\blacksquare ; \Delta t = 4.00 s\)

c) จาก \(\vec{v} = \frac{d\vec{r}}{dt}\)

\(_{t = 4}\)

îĵk̂

\(\vec{v} =\frac{d}{dt}(4t^{2} + 5t + 6 )\)

\(_{t = 4}\)

îĵîĵ

\(\vec{v} = 8t + 5 = 32.0 + 5.00 m/s \;\blacksquare\)

\(_{t = 4}\)

d) จาก \(\vec{a} = \frac{d\vec{v}}{dt}\)

\(_{t = 4}\)

îĵ

\(\vec{a} =\frac{d}{dt}(8t + 5 )\)

\(_{t = 4}\)

îî

\(\vec{a} = 8 = 8.00 m/s^{2} \;\blacksquare\)

\(_{t = 4}\)