Explain how acceleration and initial velocity decides trajectory of a motion.

1. The resultant motion is linear if:

• initial velocity \(\overset\rightarrow{u}\) = 0 (starting from rest) and acceleration \(\overset\rightarrow{a}\) is in any direction.
• initial velocity \(\overset\rightarrow{u}\) ≠ 0 and acceleration a is in line with the initial velocity (same or opposite direction).

2. The resultant motion is circular if initial velocity \(\overset\rightarrow{u}\) ≠ 0 and acceleration \(\overset\rightarrow{a}\) is perpendicular to the velocity throughout.

3. The resultant motion is parabolic if the initial velocity \(\overset\rightarrow{u}\) is not in line with the acceleration \(\overset\rightarrow{a}\) and \(\overset\rightarrow{a}\) = constant.

e.g., trajectory of a projectile motion.

4. Similarly, various other combinations of initial velocity and acceleration will result into more complicated motions.