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A lightyear is defined as the distance that light travels in a year

(i) calculate, in meters, the distance of $1$ light year, give your answer In standard form( speed of light=$3\times10^8$ m/s, numbers of days in a year = $365$

(ii) the nearest star from earth, alpha Centauri, is approximately $4.24$ light years away. Calculate in years, the time taken for a spaceship traveling at $1.2\times10^5$ m/s to reach the nearest star

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What have you tried so far? –  Sujaan Kunalan Jun 17 '13 at 19:04
    
I did (i) but I'm stuck at(ii) –  user82844 Jun 17 '13 at 19:14
    
That's not the speed of light. The speed of light is $2.99792458\times 10^8 \mathrm m/\mathrm s$, exactly. –  dfeuer Jun 17 '13 at 19:17
    
Some questions round it to 3 $\times$ 10^8 m/s –  Sujaan Kunalan Jun 17 '13 at 19:18
    
That's why we have the $\approx$ symbol. –  dfeuer Jun 17 '13 at 19:18
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2 Answers

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For part (i), you should use the relation $\text{speed}=\dfrac{\text{distance}}{\text{time}}$ and solve for $\text{distance}$ where $\text{speed}=3\times10^8\text{m/s}$ and $\text{time}=1\times 365\times24\times60\times60 \text{s}$.

For part (ii), once you've figured out what a light year is in metres in part (i), you can again use the relation $\text{speed}=\dfrac{\text{distance}}{\text{time}}$ and solve for time where $\text{distance}=4.24\times\text{light years in metres}$, and $\text{speed}=1.2\times10^5\text{m/s}$. Once you've obtained your time in seconds, convert it into years.

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Hint 1: For (i), you are given the speed and the time. Given the formula: time $\times$ speed = distance, can you solve it now?

Hint 2: For part (ii), convert light years into metres, and then apply the formula listed above.

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