Question

List I gives some physical quantites and List II gives some possible graphs

symbols have usual meaning i.e., a, v, x, t stands for acceleration, velocity, position and time for given v - x graph correct match is

• A. $I\to P,II\to P,III\to Q,IV\to Q$
• B. $I\to Q,II\to P,III\to V,IV\to S$
• C. $I\to Q,II\to P,III\to P,IV\to Q$
• D. $I\to Q,II\to P,III\to R,IV\to Q$

Answer 1

The correct option is C $I\to Q,II\to P,III\to P,IV\to Q$

$v=mx\Rightarrow a=\frac{dv}{dt}=\frac{d}{dt}mx\Rightarrow a=mv$ -- (1)
$a=m\left[mx\right]\Rightarrow a=m^{2}x$ --(2)
$v=mx\Rightarrow \frac{dx}{dt}=mx\Rightarrow \int \frac{dx}{x}=\int mdt$
$lnx=mt+c$
$\Rightarrow x=e^{(mt+c)}$ -- (3)
$a=m^{2}x=m^2{e}^{(mt+c)}$