Question

A $2.0$kg particle moving along the $x-$axis experiences the force shown in FIGURE. The particle’s velocity is $4.0$m/s at $x=0$m. What is its velocity at $x=2$m and $x=4$m?

Short answer

Particle's speed at x=2 is 5.10 m/s and at x=4 is 4 m/s

Step-by-step solution

Step 1. Given information

We have,

The mass $m=2.0$

Particle velocity$4.0$m/s at$x=0$m

Step 2. Find the particle speed

The work-kinetic theory gives

$$\begin{gathered} W=K_{final}-K_{initial} \\ {K}_{final}=W+K_{initial} \end{gathered}$$

Now,

$$\begin{gathered} \frac{1}{2}m{v^2}_{final}=W+16J \\ {v}_{final}=\sqrt{\frac{2}{m}(W+11)}=\sqrt{1k{g}^{-1}·(W+16J)} \\ x=2\Rightarrow W=10N·2m·\frac{1}{2}=10J \end{gathered}$$

Then, for x=2

role="math" localid="1648175674896" $$\begin{gathered} v_{final,x=2}=\sqrt{1k{g}^{-1}·(10J+16J)} \\ {v}_{final,x=2}=5.10m/s \\ x=4\Rightarrow W=10N·2m·\frac{1}{2}+(-10N)·2m·\frac{1}{2}=0J \end{gathered}$$

Now, for x=4

$$\begin{gathered} v_{final,x=4}=\sqrt{1k{g}^{-1}·(0J+16J)} \\ {v}_{final,x=4}=4m/s \end{gathered}$$