Accelerating at 9.8 m/s² means that every second, the speed is 9.8 m/s faster than it was a second earlier. It's not important to the problem, but this number (9.8) happens to be the acceleration of gravity on Earth.
1% of the speed of light = (300,000,000 m/s) / 100 = 3,000,000 m/s .
Starting from zero speed, moving (9.8 m/s) faster every second,
how long does it take to reach 3,000,000 m/s ?
(3,000,000 m/s) / (9.8 m/s²) = 306,122 seconds .
(That's 5,102 minutes.)
(That's 85 hours.)
(That's 3.54 days.)
Speed at the beginning . . . zero .
Speed at the end . . . 3,000,000 m/s
Average speed . . . . . 1,500,000 m/s
Distance = (average speed) x (time)
= (1,500,000 m/s) x (306,122 sec) = 4.592 x 10¹¹ meters
= 459 million kilometers
That's like from Earth
to Sun
to Earth
to Sun.
