BITSAT 2018 Slot 2 Solved Paper

We know, instantaneous displacement,
x=r‌sin‌ω‌t
∵ Instantaneous velocity, v=

dx

dt

=rω‌cos‌ω‌t
∵ Instantaneous acceleration,
a=

dv

dt

=−rω2‌sin‌ω‌t=−ω2x
So,

aT

x

=

−ω2x×T

x

=−ω2T=

−4π2

T2

×T
=

−4π2

T

=constant

aT

V

=

−ω2r‌sin‌ω‌t×T

ωr‌cos‌ω‌t

=−ωT‌tan‌ω‌T
=−

2π

T

×T‌tan‌ω‌t= not constant
Similarly, aT+2πv and a2T2+4π2v2is also not constant,
i.e. both are function of t.