Question

The force displacement graph of a particle starting from rest is given in the figure shown. The kinetic energy of a particle at $x=3m$ is

• A. $6.5J$
• B. $7.5J$
• C. $6J$
• D. $5J$

Answer 1

The correct option is A

$6.5J$

Step 1: Given data

It is a force versus displacement graph

The particle is starting from the rest

$F=$Force

$X=$Displacement

$W=$Work done

$KE=$Kinetic energy

In graph

$$\begin{gathered} X=2m,F=2N \\ X=3m,F=3N \end{gathered}$$

Step 2: To find the kinetic energy of the particle at point $x=3$

From the graph, we know,

The area under the graph is work done

$W=$ Area of a square having $2m$ as length and $2N$ as breadth $+$ Area of trapezium bases $\left(2m,3m\right)$ and height $\left(3N-2N=1N\right)$

$\begin{array}{rcl}W& =& 2\times 2+\frac{1}{2}\times \left(2+3\right)\times 1\\ W& =& 4+2.5\\ & =& 6.5J\end{array}$

We know $W=KE$

$KE=6.5J$

Hence the kinetic energy of a particle at $x=3m$ is $\mathbf{6}\mathbf{.}\mathbf{5}\mathbf{}\mathit{J}$

Therefore, the correct answer is option A.