Match the relations in Column-$I$ with the equations in Column-$II$ for uniformly accelerated motion.
Column-$I$ Column-$II$ $(1)$ Velocity-time relation $(a)$ $v = v_0 + at$ $(2)$ Velocity-displacement relation $(b)$ $S = v_0t + \frac{1}{2}at^2$ $(c)$ $v^2 = v_0^2 + 2as$
| Column-$I$ | Column-$II$ |
|---|---|
| $(1)$ Velocity-time relation | $(a)$ $v = v_0 + at$ |
| $(2)$ Velocity-displacement relation | $(b)$ $S = v_0t + \frac{1}{2}at^2$ |
| $(c)$ $v^2 = v_0^2 + 2as$ |
(A) The equations of motion for constant acceleration are:
$1$. Velocity-time relation: $v = v_0 + at$. Thus,$(1) \to (a)$.
$2$. Position-time relation: $S = v_0t + \frac{1}{2}at^2$.
$3$. Velocity-displacement relation: $v^2 = v_0^2 + 2as$. Thus,$(2) \to (c)$.
Therefore,the correct matching is $(1-a, 2-c)$.
$1$. Velocity-time relation: $v = v_0 + at$. Thus,$(1) \to (a)$.
$2$. Position-time relation: $S = v_0t + \frac{1}{2}at^2$.
$3$. Velocity-displacement relation: $v^2 = v_0^2 + 2as$. Thus,$(2) \to (c)$.
Therefore,the correct matching is $(1-a, 2-c)$.
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