Question

A variable force, given by the 2-dimensional vector, acts on a particle. The force is in mewton 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. -7 J
• B. Zero
• C. +7J
• D. +19 J

Answer 1

Answer: (C)

+7J

Answer 2

$\overrightarrow { \mathrm { r } } = x \hat { \dot { i } } + y \hat { \dot { i } }$

Work done,

$= \int _ { ( 2,3 ) } ^ { ( 3,0 ) } 3 x ^ { 2 } d x + 4 d y = \int _ { ( 2,3 ) } ^ { ( 3,0 ) } d \left( x ^ { 3 } + 4 y \right)$

According to work-energy theorem.

Change in the kinetic energy = work done, W = +7J