Problem 2.27 Challenge

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

\(\int d\vec{r} = \int \vec{v}dt\)

\(_{4}\)

\(\Delta \vec{r}=\int (3t^{2}+4t+5)dt\)

\(_{0}\)

\(_{4}\)

\(\Delta \vec{r}=t^{3}+2t^{2}+5t=116m\;\blacksquare\)

\(_{0}\)

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

\(\vec{v}_{av}=\frac{116}{4.00 - 0}= 29.0 m/s \;\blacksquare\)

c) จาก \(v(4.00) = 3(4.00)^{2} + 4(4.00) + 5 = 69.0 m/s \;\blacksquare\)

d) จาก \(\vec{a}_{av}=\frac{\Delta \vec{v}}{\Delta t}=\frac{\vec{v}(4.00) - \vec{v}(0)}{4.00 - 0}=\frac{69.0 - 5}{4.00 - 0}= 16 m/s^{2} \;\blacksquare\)

e) จาก \(\vec{a} = \frac{d\vec{v}}{dt}=\frac{d(3t^{2} + 4t + 5)}{dt}= 6t + 4= 28 m/s^{2}\;\blacksquare\)

\(_{t = 4t = 4t = 4}\)