Question

A body of mass 0.5 travels in a straight line with velocity v=kx where k=5^-1. What is the work done by the net force during its displacement from x=0 to x=2m?

Answer 1

body travels in straight line with velocity

v = ax^{3/2}

where a = 5 m-½/s

velocity at x = 0

u { initial velocity } = a(0)^{3/2} = 0

velocity at x = 2m

V { final velocity } = a(2)^{3/2} = 5× (8)½ = 10√2 m/s

we know,

according to Work-energy theorem

workdone = change in kinetic energy

workdone = 1/2 m( Vf² - Vi²)

= 1/2 × 0.5 × { 200 - 0}

=50 Joule

hence, workdone by net Force during 0 ≤ x ≤ 2 is 50 joule