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Question

How much time would be required for a starship to reach Proxima Centauri, the star closest to the Sun, at a distance of $L=4.244$ light years(**ly**)? Assume that it starts from rest, maintains a comfortable acceleration magnitude of $1.000 \mathrm{~g}$ for the first $0.0450 \mathrm{~y}$ and a deceleration (slowing) magnitude of $1.000 \mathrm{~g}$ for the last $0.0450 \mathrm{~y}$, and cruises at constant speed in between those periods.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 10**Givens**

- $L=4.244\ \text{ly}=4\cdot 10^{16}\ \text{m}$ - the distance to Proxima Centauri
- $a_1=a_3=1\ g=9.81\ \frac{\text{m}}{\text{s}^2}$ - the accelerations in the first and the third part
- $\Delta t_1=\Delta t_3=0.045\ \text{y}=1.42\cdot 10^6\ \text{s}$ - the duration of the first and the third part

**Required**

- $\tau$ - the time it takes to reach Proxima Centauri

*How can we use the known expressions for the speed and the distance travelled by the ship in order to find $\tau$?*

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