Refer to graph in figure. Match following Graph Characteristics (A) (i) has v > 0 and a

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2.Motion in Straight Line

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Refer to the graph in figure. Match the following

Graph Characteristics

$(A)$ $(i)$ has $v > 0$ and $a < 0$ throughout

$(B)$ $(ii)$ has $x > 0,$ throughout and has a point with $v = 0$ and a point with $a = 0$

$(C)$ $(iii)$ has a point with zero displacement for $t > 0$

$(D)$ $(iv)$ has $v < 0$ and $a > 0$

Option A

Option B

Option C

Option D

Solution

We have to analyse slope of each curve i.e., $\frac{d x}{d t}$ For peak points $\frac{d x}{d t}$ will be zero as $x$ is maximum at peak points.

For graph $(a)$, there is a point $(B)$ for which displacement is zero. So, a matches with $(iii)$

In graph (b), $x$ is positive $(>0)$ throughout and has a point $\mathrm{B}_{1}$ with $\mathrm{V}=\frac{d x}{d t}=0$. As at point of curvature changes $a=0$, So $b$ matches with $(ii)$

In graph $(c)$, slope $\mathrm{V}=\frac{d x}{d t}$ is negative hence, velocity will be negative. So, it matches with (iv)

In graph $(d)$, as slope $\mathrm{V}=\frac{d x}{d t}$ is positive hence, $\mathrm{V}>0$

Hence, $d$ matches with $(i)$

Standard 11

Physics

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(KVPY-2013)

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