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  4. Velocity (v) versus displacement (x) plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration (a) as a function of displacement (x) is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-sonlwuvbciuu.png />

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Q. Velocity $\left(v\right)$ versus displacement $\left(x\right)$ plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration $\left(a\right)$ as a function of displacement $\left(x\right)$ is

Question

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

The given graph
$v=Kx$ .....(i)
Solution
$\frac{d v}{d t}=K \, . \, v$ (from the equation (i))
$\frac{d v}{d t}=K.\left(K x\right)=K^{2}x$
$a=K^{2}x$
and $v= \, -Kx+v_{0}$
$\frac{d v}{d t}= \, -K.v= \, -K\left(- K x + v_{0}\right)$
$a=K^{2}x-Kv_{0}$ .......(ii)
So, according to the equation (ii).
Solution