UPSEE 2019 Solved Paper

Given, retardation a=−kx
Here, x is the displacement of the particle.
As we know that, a=

dv

dt

=

dv

dx

.

dx

dt

=−kx
So, v.

dv

dx

=−kx[∵

dx

dt

=v]
Let for any displacement from 0 to x, velocity changes from v0 to v.
⇒

v

∫

v0

vdv=−k‌

x

∫

0

xdx
⇒[

v2

2

]v0v=−

kx2

2

⇒

m(v2−v02)

2

=−

mkx2

2

⇒ΔKE∝x2
Hence, the correct option is (c).