Question

A rock of mass m slides down with an initial velocity v₀. A retarding force F = -k v^1/2 acts on the body. The velocity at any instant is given by

• A. v = v₀ - $\frac { \mathrm { kt } } { \mathrm { m } }$
• B. v = v₀ - $\left( \frac { \mathrm { kt } } { \mathrm { m } } \right) ^ { 2 }$
• C. $\sqrt { \mathrm { v } } = \sqrt { \mathrm { v } _ { 0 } } - \frac { \mathrm { kt } } { \mathrm { m } }$
• D. None of these

Answer 1

Answer: (C)

$\sqrt { \mathrm { v } } = \sqrt { \mathrm { v } _ { 0 } } - \frac { \mathrm { kt } } { \mathrm { m } }$

Answer 2

$\frac { \mathrm { mdv } } { \mathrm { dt } } = - \mathrm { kv } ^ { 1 / 2 }$

or $\int _ { \mathrm { v } _ { 0 } } ^ { \mathrm { v } } \frac { \mathrm { dv } } { \mathrm { v } ^ { 1 / 2 } } = - \int _ { 0 } ^ { \mathrm { t } } \frac { \mathrm { kdt } } { \mathrm { m } }$

or $\sqrt { \mathrm { v } } = \sqrt { \mathrm { v } _ { 0 } } - \frac { \mathrm { kt } } { \mathrm { m } }$