Question

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled $3m$ is

• A. $5J$
• B. $2.5J$
• C. $6.5J$
• D. $4J$

Answer 1

The correct option is C $6.5J$

Formula Used: $W=\Delta KE$
Applying work energy theorem Work done by force on the particle
$=$ Change in $KE$

Work done = Area under $F-x$ graph

$W=\int F.dx$

$=2\times 2+\frac{(2+3)\times 1}{2}$

$W=K{E}_{final}-K{E}_{initial}=6.5$

$K{E}_{initial}=0$

$K{E}_{final}=6.5J$

Final Answer: (a)