Question

Velocity versus displacement graph of a particle moving in a straight line is as shown in figure. The acceleration of the particle is:

• A. Increases linearly with $x$
• B. Constant
• C. Increases parabolically with $x$
• D. None

Answer 1

The correct option is A Increases linearly with $x$


From the graph, velocity-displacement equation can be written as:
$v=v_o+\alpha x\dots \left(1\right)$
Here, $v_o$ and $\alpha$ are positive constants.
Differentiating Eq. (1) with respect to $x$ we get, $\frac{dv}{dx}=\alpha =constant$
Acceleration of the particle can be written as
$a=\frac{dv}{dt}$
Or, $a=v\frac{dv}{dx}$
$a=(v_o+\alpha x)\alpha =v_0\alpha +{\alpha }^{2}x$
Above equation signifies linear relationship of $a$ and $x$. Thus, acceleration increases linearly with $x$.