Question

Force acting on a particle moving in a straight line varies with the velocity of the particle as F is equals to k b v real case a constant

Answer 1

Answer:

Correct option is D)

Given that,

Force F=KV

Velocity=V

We know that,

F=Ma

Now,

Ma=KV

M(

dt

dV

)=KV

MdV=KVdt

Multiply by v in both side

MVdV=KV

2

dt

On integrating both side

v

1

∫

v

2

MVdV=

0

∫

t

KV

2

dt

M[

2

V

2

2

−

2

V

1

2

]=KV

2

t

2

M

[V

2

2

−V

1

2

]=KV

2

t

Now, the change in K.E

Now, from work energy theorem

Change in energy = work done

K.E=KV

2

t

Hence, the work done is KV

2

t