Kinematics 4 Question 1
1. A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $X$-axis. Identify all figures that correctly represent the motion qualitatively. ( $a=$ acceleration, $v=$ velocity, $x=$ displacement, $t=$ time)
(2019 Main, 8 April II)
(B)
(a) $(A)$
(b) $(A),(B),(C)$
(c) $(B),(C)$
(d) $(A),(B),(D)$
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Solution:
- Since, the particle starts from rest, this means, initial velocity, $u=0$
Also, it moves with uniform acceleration along positive $X$-axis. This means, its acceleration $(a)$ is constant.
$\therefore$ Given, $a-t$ graph in (A) is correct.
As we know, for velocity-time graph, slope $=$ acceleration.
Since, the given $v-t$ graph in (B) represents that its slope is constant and non-zero.
$\therefore$ Graph in (B) is also correct.
Also, the displacement of such a particle w.r.t. time is given by
$$ \begin{aligned} x & =u t+\frac{1}{2} a t^{2} \\ & =0+\frac{1}{2} a t^{2} \Rightarrow x \propto t^{2} \end{aligned} $$
So, $x$ versus $t$ graph would be a parabola with starting from origin.
This is correctly represented in displacement-time graph given in (D).
