Question

Figure shows the variation of a force $F$ acting on a particle along $x-$ axis. If the particle begins at rest at $x=0$, what is the particle's coordinate when it again has zero speed ?

• A. $x=3$
• B. $x=6$
• C. $x=5$
• D. $x=7$

Answer 1

The correct option is B $x=6$

Using work energy theorem
$W_F=\Delta KE$
$\Rightarrow \underset{x_1}{\overset{x_2}{\int }}Fdx=\Delta KE$
Given that $\Delta KE=0$ (Both initial and final velocity =0)
$\Rightarrow \int Fdx=0=$ Area under $F-x$ graph
$\Rightarrow$ Positive area = Negative area

Positive area = Area from $x=0$ to $x=3$
$=10+20+5=35$ sq.units

Negative area from $x=3$ to $x=6$
$=10+20+5=35$ sq. units

So, at $x=6$, Total area $=0$