Question

A variable force, given by the 2-dimensional vector $\overrightarrow{F}=(3x^2\hat{i}+4\hat{j})$, acts on a particle. The force is in newton and $x$ is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates $(2,3)$ to $(3,0)?$ (The coordinates are in metres)

• A. $-7J$
• B. zero
• C. $+7J$
• D. $+19J$

Answer 1

The correct option is C $+7J$

The change in kinetic energy is equal to work done on the particle. On x-axis, the particle changes its position from $2m$ to $3m$. On y-axis, the particle changes its position from $3m$ to $0m$.

$W={\int }_2^{3}3x^{2}dx+{\int }_3^{0}4dy$
$W=7J$