Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

Question

Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-hkkmpb5uj0dpw9iy.jpg" /> (A) increases linearly (B) decreases linearly (C) is constant (D) increases parabolically

Tardigrade Admin · Accepted Answer

From the acceleration-velocity graph, we have

a = k v

where

k

is a constant which represents the slope of the given line.
As,

a = v \frac{d v}{d s},

so

v \frac{d v}{d s} = k v

or

\frac{d v}{d s} = k = a

constant
Thus, the slope of the velocity-displacement graph is the same as that of acceleration-velocity. Which is constant.

Q. Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

increases linearly

decreases linearly

is constant

increases parabolically

From the acceleration-velocity graph, we have a=kv where k is a constant which represents the slope of the given line. As, a=vdsdv​, so vdsdv​=kv or dsdv​=k=a constant Thus, the slope of the velocity-displacement graph is the same as that of acceleration-velocity. Which is constant.