1. Tardigrade
  2. Question
  3. Physics
  4. A variable force, given by the two dimensional vector F=(3x2 hati+4 hatj) 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).

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Q. 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).

Motion in a Plane

Solution:

Given, two dimensional force
$ F = 3x^2 \hat i + 4 \hat j$
$40mm r = x \hat i + y \hat j$
$ 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 + 4 \, dy)$
$ = [x^3]_2^3 + 4[y]_3^0 = (27 - 8) + 4 (-3)$
$ = 19 - 12 = 7 J$