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

Answer 1

The correct option is A $6.5J$

According to Work Energy Theorem,
Work done by force on the particle $=$ Change in $KE$
Work done $=$ Area under $F-x$ graph
$=\int F.dx$
$=2\times 2+\frac{(2+3)\times 1}{2}=6.5J$
$W=K{E}_{final}-K{E}_{initial}=6.5J$
$K{E}_{initial}=0$
$\therefore K{E}_{final}=6.5J$