Question

An object of mass m has a speed v, as it passes through the origin on its way along +x-axis. It is subjected to a retarding force given by F= -Ax. Here A, is a positive constant. Find its x-coordinate when it stops.

Answer 1

Answer on Question #45885, Physics, Mechanics | Kinematics | Dynamics

An object of mass $m$ has a speed $v$, as it passes through the origin on its way along $+x$-axis. It is subjected to a retarding force given by $F = -Ax$. Here $A$ is a positive constant. Find its $x$-coordinate when it stops.

Solution:

The kinematic equation that describes an object's motion is:

$$2ax = v_f^2 - v_0^2$$

where $a$ is acceleration, $x$ is coordinate, $v_0$ is initial velocity and $v$ is final velocity.

$v_0 = v$ and $v_f = 0$.

Newton's Second Law

$$F = ma$$

So,

$$ma = -Ax$$

Thus, the acceleration is

$$a = -\frac{Ax}{m}$$

So,

$$-2\frac{Ax}{m}x = -v^2$$ $$x^2 = \frac{mv^2}{2A}$$ $$x = v \sqrt{\frac{m}{2A}}$$

Answer: $x = v \sqrt{\frac{m}{2A}}$

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