A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light.

The detailed steps are as shown below

Recalling from F = ma a = F/m but magnitude of force F = √ [ 1 - v²/c²]

but acceleration twice as great as the force required to produce the same acceleration;

2m = m / √[ 1 - v²/c²] 2 = 1 / √ [ 1 - v²/c²] square both sides;

4 = 1 / [ 1 - v²/c²]

1/4 = 1 - v²/c²

v²/c² = 3/4

v/c = √ [3/4]

v = 0.87c

but speed of light c = 3 x 10^8m/s

v = speed of the particle = 0.87 (3 x 10^8m/s)

v = 2.61m/s