The kinetic energy K of a particle moving in a straight line depends on the distance s as K=as2 . The force acting on the particle is (where a is a constant)

Question

The kinetic energy K of a particle moving in a straight line depends on the distance s as K=as2 . The force acting on the particle is (where a is a constant) (A) 2as (B) as (C) 2a (D) √ textitas2

Tardigrade Admin · Accepted Answer

Here kinetic energy textK = (1/2) textmv2 = texta text texts 2 â´ mv2 = 2as2 ...(i) Differentiating eqn (i) w.r.t. to time t, we get 2 textmv ( textdv/ textdt) = 4 textas ( textds/ textdt) = 4 textasv textor textm ( textdv/ textdt) = 2 textas

Q. The kinetic energy $K$ of a particle moving in a straight line depends on the distance s as $K = a s^{2}$ . The force acting on the particle is

(where $a$ is a constant)

$2 a s$

$a s$

$2 a$

$as^{2}$

Here kinetic energy $K = \frac{1}{2} mv^{2} = a s^{2}$
∴ mv² = 2as² ...(i)
Differentiating eqn (i) w.r.t. to time t, we get
$2 mv \frac{dv}{dt} = 4 as \frac{ds}{dt} = 4 asv or m \frac{dv}{dt} = 2 as$

Q. The kinetic energy K of a particle moving in a straight line depends on the distance s as K=as2 . The force acting on the particle is (where a is a constant)

2as

as

2a

as2​