Question

An object of mass $5\text{kg}$ is acted upon by a force that varies with position of the object as shown by the graph. If the object starts from rest at a point $x=0$, what is its speed at $x=50\text{m}$

• A. $12.2{\text{ms}}^{-1}$
• B. $18.2{\text{ms}}^{-1}$
• C. $16.4{\text{ms}}^{-1}$
• D. $20.4{\text{ms}}^{-1}$

Answer 1

The correct option is A $12.2{\text{ms}}^{-1}$

From work energy theorem:
Change in kinetic energy $=$ work done

$W_{net}=\Delta KE$

But, Work done $=$ area under $F-x$ graph

$\therefore \frac{1}{2}\times 5\times v^2=10\times 25+\frac{1}{2}\times (50-25)\times 10$

$\Rightarrow \frac{1}{2}\times 5\times v^2=375$

$v=12.2\text{m/s}$

Why this question? Graphically, area under the $F-x$ graph is equal to the work done. Key concept- Work energy theorem states that the total work done on a system equals the change in its kinetic energy.