Ncert Exercises & Solutions

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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