Question

In a uniform electric field, a point charge of mass $m$ and charge $q$ is released from rest. If there are no other forces acting on the particle, then which of the following graphs, correctly show the dependence of the particles speed $v$ on the distance $x$ travelled by it?

• A. Graph 1
• B. Graph 2
• C. Graph 3
• D. Graph 4

Answer 1

Answer: (D)

Graph 4

Answer 2

Using kinematics under constant acceleration:

• The electric force $F=qE$ is constant, so the acceleration $a = F/m = qE/m$ is constant.
• From kinematics, for motion from rest with constant acceleration,

$$v^2 = 2ax \quad\Longrightarrow\quad v = \sqrt{2ax}\propto \sqrt{x}.$$

• The function $v\sim\sqrt{x}$ is concave upward, starting with infinite slope at $x=0$ and gradually flattening less steeply as $x$ increases.
• Among the given sketches, Graph 4 matches the shape of $v\propto\sqrt{x}$. It shows $v$ rising from zero with a continuously increasing slope that diminishes in curvature, exactly the $\sqrt{x}$ profile.