Question

A spaceship starting from a resting position accelerates at a constant rate of 9.8 meters per second per second. How long and how far will it take the spaceship to reach a speed of 1 percent the speed of light (300,000,000 m/s)
HOW LONG ANSWER CHOICES
A. 3.5 days
B. 35.4 days
C. 354 days
D. 3403 days
HOW FAR ANSWER CHOICES
A. 3.1 × 106 m
B. 2.94 × 108 m
C. 7.8 × 1010 m
D. 4.6 × 1013 m
30 POINTS

Answer 1

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.