Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :-

Question

Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :- (A) √v (B) √[s](v/2) (C) v(5/3) (D) v2

Tardigrade Admin · Accepted Answer

Power =Fv propto v ⇒ mv(d v/d t)=kv, where k= constant ⇒ m dv.dt=k ⇒ mv(d v/d x)=k ⇒ vdv=(k d n/m)

Q. Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :-

$v$

$s \frac{v}{2}$

$v^{\frac{5}{3}}$

$v^{2}$

Power $= F v \propto v$
$\Rightarrow m v \frac{d v}{d t} = k v,$ where $k =$ constant
$\Rightarrow m d v . d t = k \Rightarrow m v \frac{d v}{d x} = k$
$\Rightarrow v d v = \frac{k d n}{m}$

Q. Consider a machine delivering power to a body which is proportional to velocity of the body. Suppose the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to (choose the correct option from the following) :-

v​

s2v​​

v35​

v2

Power =Fv∝v ⇒mvdtdv​=kv, where k= constant ⇒mdv.dt=k⇒mvdxdv​=k ⇒vdv=mkdn​

$v$

$s \frac{v}{2}$

$v^{\frac{5}{3}}$

$v^{2}$

Power $= F v \propto v$
$\Rightarrow m v \frac{d v}{d t} = k v,$ where $k =$ constant
$\Rightarrow m d v . d t = k \Rightarrow m v \frac{d v}{d x} = k$
$\Rightarrow v d v = \frac{k d n}{m}$