Question

0:01
5. The retardation of the particle is given as kv
vhere k is constant. After how much time taken
Velocity decreases by 50%.​

Answer 1

Answer:

$\frac{1}{k}ln2$

Explanation:

let initial velocity at time t=0 is v then we need to find the time in which its velocity becomes v/2, let that time be t

Given retardation = kv

or a = -kv

or, dv/dt = -kv

or, dv/v = -kdt

Integrating both sides

$\int\limits^\frac{v}{2} _v {\frac{1}{v} } \, dv=-k\int\limits^t_0 {} \, dt$

or, $ln\frac{v}{2} -lnv=-kt$

or, $t=\frac{1}{k}ln2$