Question

Starting from rest, a partricle is moving along x-axis. The variation of force $F$ with position $x$ is shown in figure. Find the $KE$ of the particle when it has moved from $x=1\text{m}$ to $x=3\text{m}$.

• A. $3.3\text{J}$
• B. $4\text{J}$
• C. $5\text{J}$
• D. $4.2\text{J}$

Answer 1

The correct option is C $5\text{J}$


From work energy theorem:
$W_{\text{net}}=\Delta KE...\left(i\right)$
Initially the particle was at rest $K{E}_i=0$
Let final kinetic energy be $K{E}_f$
$\Rightarrow \Delta KE=K{E}_f-0=K{E}_f...\left(ii\right)$
From $\left(i\right)$ & $\left(ii\right)$ Eq:
$W_{\text{net}}=K{E}_f....\left(iii\right)$

Also, $W_{\text{net}}=$ Area under $F-x$ curve
$\Rightarrow W_{\text{net}}=\text{Area of rectangle+ Area of trapezium}$
$=(1\times 2)+\frac{1}{2}\times (2+4)\times 1$
$\Rightarrow W_{\text{net}}=5\text{J}$

Putting the value of $W_{\text{net}}$ in Eq. $\left(iii\right)$,
$\therefore K{E}_f=5\text{J}$