In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | The acceleration of the particle is zero. |
| 2. | The acceleration of the particle is increasing. |
| 3. | The acceleration of the particle is necessarily in the plane of motion. |
| 4. | The particle must be undergoing a uniform circular motion. |
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.
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