UPSEE Solved Model Paper 7

Given a = - kx
a =

dv

dt

=

dv

dx

.

dx

dt

= - kx
or

vdv

dx

= - kx
or v dv = - kx dx
Let for any displacement from 0 to x, the velocity changes from v0 to v.
⇒

v

∫

v0

vdv = -

x

∫

0

k x dx
or

v2−v02

2

= −

kx2

2

or m(

v2−v02

2

) = −

mkx2

2

or ΔK α x2 (ΔK is loss in KE)