Question

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x=0$ has kinetic energy of $25J$, then the kinetic energy of the particle at $x=16m$ is

• A. $45J$
• B. $30J$
• C. $70J$
• D. $20J$

Answer 1

The correct option is A $45J$

Given :

$K.E_{x=0}\Rightarrow 25J$

Work done =$F_x$ = area under $F-x$ curve.

hence here area under the graph is :

from

$x=0$ to $x=6m\Rightarrow A_1=\frac{1}{2}\times 6\times 10=30$

$x=6$ to $x=10m\Rightarrow A_2=4\times (-5)=-20$

$x=10$ to $x=14m\Rightarrow A_3=4\times 5=20$

$x=14$ to $x=16m\Rightarrow A_4=2(-5)=-10$

total area $A=A_1+A_2+A_3+A_4=30-20+20-10=20$

hence $\text{Work=20J}$

Now, from work energy theorem; work done = change in K.E.

So, $K.E_f-K.E_i=work=20J\Rightarrow K{E}_f-25J=20J$

$\Rightarrow K{E}_f=20+25=45J$

hence K.E at $x=16$ is $45J$

So (A) option is correct.