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 - t graph correct match is? Where at t = 0, particle is at some positive position

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

Answer 1

The correct option is A $I\to U,II\to U,III\to U,IV\to Q$

$v=mt\Rightarrow a=\frac{dv}{dt}=m$
here m is constant so acceleration is constant.
$v=\frac{dx}{dt}\Rightarrow {\int }_{x_0}^{x}dx={\int }_0^{t}mtdt$
$x-x_0=\frac{m{t}^2}{2}\Rightarrow x=\frac{m{t}^2}{2}+x_0$
So, x-t graph is a parabola.