The accompanying graph of position x versus t | vedclass

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Question

(D) The correct option is $(d)$.$1$. The velocity $v$ of a particle is given by the slope of the position-time $(x-t)$ graph,i.e.,$v = \frac{dx}{dt}$.

Vedclass · Accepted Answer

$a=p-q t$

Vedclass · Answer

(D) The correct option is $(d)$.$1$. The velocity $v$ of a particle is given by the slope of the position-time $(x-t)$ graph,i.e.,$v = \frac{dx}{dt}$.$2$. Initially,the slope of the $x-t$ graph is negative and increasing (becoming less negative),then it becomes positive and increases,and finally,it becomes positive and decreases (approaching zero slope at the peak).$3$. The acceleration $a$ is the rate of change of velocity,i.e.,$a = \frac{dv}{dt}$,which corresponds to the slope of the velocity-time $(v-t)$ graph.$4$. From the given $x-t$ graph,the curvature changes from concave up to concave down. This implies that the acceleration is initially positive (as the velocity increases) and eventually becomes negative (as the velocity decreases).$5$. Among the given options,the expression $a = p - qt$ (where $p, q > 0$) represents an acceleration that starts at a positive value $p$ and decreases linearly with time $t$,eventually becoming negative. This matches the physical behavior observed in the graph.

The accompanying graph of position $x$ versus time $t$ represents the motion of a particle. If $p$ and $q$ are both positive constants,the expression that best describes the acceleration $a$ of the particle is

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