Problem 2.28 Challenge

จาก \(\vec{a} = 10 - 2t\)

\(\frac{d\vec{v}}{dt}= 10 - 2t\)

\(\int d\vec{v} = \int (10 - 2t)dt\)

\(\vec{v}(t) = 10t - t^{2} + c\)

จาก \(t = 0 s\) วัตถุมีความเร็วเท่ากับ \(15.0 m/s\)

จะได้ \(15.0 = 10(0) - (0)^{2} + c\)

\(c = 15.0\)

\(\therefore \vec{v}(t) = 10t - t^{2} + 15.0\)

จาก \(|\vec{a}_{av}| = |\frac{\Delta \vec{v}}{\Delta t}| = |\frac{\vec{v}(5.00) - \vec{v}(0)}{5.00 - 0}| =\frac{40.0 - 15.0}{5.00 - 0}= 5.00 m/s^{2} \;\blacksquare\)

จาก \(\vec{v}(t) = 10t - t^{2} + 15.0\)

\(\frac{d\vec{r}}{dt}= 10t - t^{2} + 15.0\)

\(_{5}\)

\(\int d\vec{r}=\int (10t-t^{2}+15.0)dt\)

\(_{0}\)

\(\Delta \vec{r} = 5t^{2} -\frac{t^{3}}{3}+ 15t= 158 m\)

\(_{t = 5}\)

\(\therefore |\Delta \vec{r}| = 158 m \;\blacksquare\)