Question

In $FIGUREEX10.28$, what is the maximum speed a $200g$particle could have at $x=2.0m$.

It never reach $x=6.0m$?

Short answer

Particle's maximum speed is$6.32m/s$.

Step-by-step solution

Speed : 

It is the change in an object's location with regard to time.

Explanation : 

Particle's mass $$\begin{gathered} m=200gm \\ =0.2kg \end{gathered}$$,

Formula to determine the kinetic energy of a particle ,

$KE=\frac{1}{2}m{v}^2$

$KE$= kinetic energy,

$m$= particle's mass

$v$= particle's velocity.

Consider the graph of potential energy against distance,

The peak of the curve between $$\begin{gathered} x=2mand \\ x=6m \end{gathered}$$.

It occurs at $x=4m$.

Particle's kinetic energy at $x=4m$must be $0$.

It is if the particle is not allowed to reach at $x=6m$.

The potential energy difference of localid="1647865759613" $$\begin{gathered} x=4mand \\ x=2m \end{gathered}$$would be the particle's maximum speed so that it can never reach at $x=6m$.

Potential energy difference,

$$\begin{gathered} KE=8-4 \\ =4J \end{gathered}$$

Particle's maximum velocity,

$$\begin{gathered} KE=\frac{1}{2}m{v}^2 \\ 4=\frac{1}{2}\times 0.2\times v^2 \\ v=6.32m/s \end{gathered}$$

Hence, maximum speed of particle is$6.32m/s$.