Question

A variable force, given by the 2-dimensional vector
F(3x?î+4h) , 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):
​

Answer 1

Answer:

Explanation:

A variable force acts on a particle is F=3x²i+4h

=> The change in the kinetic  energy of the particle is equal to the work done

Thus, displacement vector D=(3−2)i−3h=i−3h

magnitude of displacement is equals to √10

Thus, unit vector in the direction of dx = i−3h /√10

=> Work done in x direction, Wx:

Wx = $\int\limits^3_2 {3x^2} \, dx$

=27−8

=19 J 

=> Work done in y direction, Wy:

Wy= (4) * (−3) = −12 J

WD =19 − 12 = 7 J

Thus, he change in the kinetic  energy of the particle as it moves from the point with  given coordinates is 7 J .