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2.Motion in Straight Line
medium
Acceleration versus velocity graph of a particle moving in a straight line starting from rest is as shown in figure. The corresponding velocity-time graph would be
A
B
C
D
Solution
The given graph is of the form $y=m x$
So, here $a=m v$ [where $m$ is negative] $\Rightarrow \frac{d v}{d t}=m v$
$\Rightarrow \frac{d v}{v}=m d t$
$\Rightarrow v=e^{m t}$
as $m$ is negative. So, $v=e^{-k t}$
Required graph will be Option$'D’$
So, here $a=m v$ [where $m$ is negative] $\Rightarrow \frac{d v}{d t}=m v$
$\Rightarrow \frac{d v}{v}=m d t$
$\Rightarrow v=e^{m t}$
as $m$ is negative. So, $v=e^{-k t}$
Required graph will be Option$'D’$
Standard 11
Physics
