TS EAMCET 5 May 2018 Shift 2 Solved Paper

The expression for the resistive force is given by,
FR=−kv

1

3

The expression for retardation of bullet is given as,
a=

dv

dt

dv

dt

=−

k

m

v

1

3

dv

dx

.

dx

dt

=−

k

m

v

1

3

dv

dx

.v=−

k

m

v

1

3

This implies,
v

2

3

dv=−

k

m

dx
Integrate the above equation on both sides.

0

∫

v0

v

2

3

dv=−

k

m

‌

s

∫

0

dx
[

3

5

v

5

3

]v00=−

k

m

[x]0s
−

3

5

v

5

3

=−

k.s

m

Therefore, s∝v

5

3

.