Question

At the high velocity, drag force is proportional to the squared velocity of a particle as kv^2. Find its acceleration when a falling speed becomes half its terminal velocity. 

Answer 1

Gives

Drag force

F_D=$\frac{1}{2}C\rho Av^2$

According to question

$F_D=kv^2$

Newton's 2^ndlaw

F=Ma

Both force are equal

$Ma=kv^2$

$a=\frac{kv^2}{M}$

When

$v'=\frac{v}{2}$

$a'=?$

$a'=\frac{k(\frac{v}{2})^2}{M}=\frac{kv^2}{4M}=\frac{a}{4}$