(Solved): 3. A car's motion consists of two consecutive parts as shown below. In the first part, it start ...

3. A car's motion consists of two consecutive parts as shown below. In the first part, it starts from rest $$(v0=0\mathrm{m}/\sec )$$ with an acceleration of $$a_1=5.00\mathrm{m}/{\mathrm{s}}^2$$ and travels a distance of $$180\mathrm{m}$$. Immediately after the first part of motion, it slows down with an acceleration of $${\mathrm{a}}_2=$$ $$2.00\mathrm{m}/{\mathrm{s}}^2$$ until it stops. Find the total distance that the car has traveled. 2. In the following figure, the magnitude of the displacement vectors are $$A=6.50\mathrm{m}$$ and $$B=$$ $$3.50\mathrm{m}$$. Vector $$\mathbf{A}$$ is directed $$37^{?}$$ with respective to the positive $$\mathrm{x}$$ direction and vector $$\mathbf{B}$$ is directed alone the positive $$\mathrm{x}$$ direction as shown below. Find the magnitude and direction of the resultant vector $$\mathbf{R}$$, that is $$\mathbf{R}=\mathbf{A}+\mathbf{B}$$.