In a two-dimensional motion, the instantaneous speed of a particle remains constant at a positive value \(v_0.\) Which of the following statements must always be true?
| 1. | The particle has zero acceleration. |
| 2. | The particle’s acceleration is increasing. |
| 3. | The particle’s acceleration always lies in the plane of motion. |
| 4. | The particle necessarily moves in a uniform circular path. |
Hint: \(v=\frac{dr}{dt}\)
Step 1: Try to prove each option wrong.
\(\text{Let velocity,}~\vec{v}=v_{x}\hat{i}+v_{y}\hat{j}\)
\(\text{Now,acceleration,}~\vec{a}=\frac{d\vec{v}}{dt}=a_{x}\hat{i}+a_{y}\hat{j}\)
As velocity is in the (x-y) plane so the acceleration of the particle is necessarily in the plane of motion.
Hence, option (3) is the correct answer.
