(g) (i) Define work done by a constant force. (1 mark) (ii) Find the work done on a particle that undergoes a displacement given by Delta overrightarrow (r)=2hat (i)+3hat (j) m due to a constant force overrightarrow (F)=5hat (i)+2hat (j)N (3 marks)

(i) Work done by a constant force is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, it can be expressed as:<br /><br />Work = Force x Displacement x cos(θ)<br /><br />where θ is the angle between the force and displacement vectors.<br /><br />(ii) To find the work done on a particle, we can use the formula:<br /><br />Work = Force dot Displacement<br /><br />Given:<br />Displacement, Δr = 2i + 3j m<br />Force, F = 5i + 2j N<br /><br />To find the dot product of the force and displacement vectors, we multiply the corresponding components of the vectors and add them together:<br /><br />F dot Δr = (5i + 2j) dot (2i + 3j)<br /> = (5 x 2) + (2 x 3)<br /> = 10 + 6<br /> = 16<br /><br />Therefore, the work done on the particle is 16 Joules.