# Relativistic speed

#### neelakash

1. The problem statement, all variables and given/known data

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 (c) 0.999 sec (d) 0.7 sec

2. Relevant equations
3. The attempt at a solution

I can safely disregard (c) 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.

But how to prove this?

Can anyone suggest anything?

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#### neelakash

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.

#### kdv

1. The problem statement, all variables and given/known data

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 (c) 0.999 sec (d) 0.7 sec

2. Relevant equations
3. The attempt at a solution

I can safely disregard (c) 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.

But how to prove this?

Can anyone suggest anything?

In relativity, $$F = \frac{dp}{dt}$$ still holds. For a constant force you have then

$$p_{final} - p_{initial} = F \Delta t$$

setting p initial equal to zero and using for the final $$p= \gamma m v$$ gives the correct answer, which is indeed b.

Note: your argument is correct and it's sufficient if all you need is to pick the correct answer quickly from a choice of answers. I just wanted to show you how to do the calculation if you needed that at some point.

Last edited:

#### neelakash

Tell me one thing.The force is specified to be 30 dyne in its own rest frame.So, is the increase of mass is to be considered at all?

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