Question

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

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

Answer 1

Answer: (C)

Given, two dimensional force
$F=3x^2\hat{i}+4\hat{j}$
$40mmr=x\hat{i}+y\hat{j}$
$dr=dx\hat{i}+dy\hat{j}$
Kinetic energy = Work done
$W=\int F.dr$
$={\int }_{(2,3)}^{(3,0)}(3x^2\hat{i}+4\hat{j}).(dx\hat{i}+dy\hat{j})$
$={\int }_2^3(3x^{2}dx+4dy)$
$=[x^3{]}_2^3+4[y{]}_3^0=(27-8)+4(-3)$
$=19-12=7J$