People hoping to travel to other worlds are faced with huge challenges. One of t

Question

People hoping to travel to other worlds are faced with huge challenges. One of the biggest is the time required for a journey. Proxima Centauri is the nearest star to us, at 4.0 x 10^16 m. Suppose you had a spacecraft at rest that could accelerate 9.8m/s^2 for a half a year, then continue at a constant speed. A) How far would you travel during the initial acceleration phase of the trip? B) At what speed and over what distance would you travel during the constant- velocity phase of the trip? C) Starting from rest, how long would it take you to reach Proxima Centauri?

Explanation / Answer

here,

a)

accelration , a = 9.8 m/s^2

time , t = half year

t = 15768000 s

the distance covered , s = u* t + 0.5 * a * t^2

s = 0 + 0.5 * 9.8 * 15768000^2

s = 1.22 * 10^15 m

the distance travelled during accelration is 1.22 * 10^15 m

b)

final velocity , v = u + a*t

v = 0 + 9.8 * 15768000

v = 1.55 * 10^8 m/s

the constant speed is 1.55 * 10^8 m/s

distance with constant speed , s' = 4 * 10^16 - 1.55 * 10^15

s' = 38.45 * 10^15 m

c)

time taken to travel at constant speed be t'

v * t' = s'

1.55 * 10^8 * t' = 38.45 * 10^15

t' = 2.48 * 10^8 s

t' = 7.86 years

the total time = 7.86 + 0.5 = 8.36 years

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