Attain Relativistic speed

[kolahalb]

A particle of mass 1 gm starts from rest and moves under the action of a force of 30
Newtons defined in the rest frame. It will reach 99% the velocity of light in time
(a) 9.9 x 10³ sec (b) 7 x 10⁴ sec © 0.999 sec (d) 0.7 sec

I can safely disregard © and (d)

( a ) can be found by kinematic calculation.But as the particle moves in relativistic speed, this classical calculation does not hold.

( b ) looks correct to me.

as speed increases,the value of m(v) also increases,thus reducing the acceleration.Thus, it takes longer time...In that respect ( b ) looks plausible.

But how to prove this?

Can anyone suggest anything?