Question

Starting from rest, you travels to north between t=0s, t=5s with an acceleration 0.4 m/s^2. Next you drive to east between t=5s and t=10s with an acceleration of 1 m/s^2. Then you drives south between t=10s and t=20s with an acceleration of 0.6 m/s^2. What is your position and velocity after 20 s?

Answer 1

Find the displacements in the respective directions assuming each change in direction begins with sudden stop to rest and new motion from rest with a new value of acceleration:

$$d_N=\dfrac{a_Nt_N^2}2=5\text{ m},\\\space\\ d_E=\dfrac{a_Et_E^2}2=12.5\text{ m},\\\space\\ d_S=\dfrac{a_St_S^2}2=30\text{ m}.\\\space\\ d=\sqrt{(d_N-d_S)^2+d_E^2}=28\text{ m},\\\space\\ \theta=\arctan\dfrac{d_S-d_N}{d_E}=63.4°\text{ S of E. }$$