Astronomy 105

Velocity, Distance and Time

5. Velocity, Distance and Time (Problems 1-1,1-2,2-1,6-2,7-3,7-4,8-1,9-3,12-1,13-4,16-2) 
   

   Probably the most important formula in the course is also one of the simplest. It simply relates velocity (speed) with distance and time:
   

    

   
   

   Since the units of velocity are length/time (m/s, miles/h, etc.), the dimensions of this formula are correct.

   Examples. If a bullet travels 1000 m in 2 s, what is its velocity?
   

   
   

   How long does it take for light to travel to Earth from the nearest star other than the Sun? Here we need to rearrange the formula:
   

   
   

   Plugging in numbers, d = 4.0 X 10¹⁶ m and v = 3.0 X 10⁸ m/s.
   

   
   

   Note that here the unit of meters cancels, leaving in the denominator which becomes seconds. Note also that I wrote the answer to two significant figures.

   One more example. If a spaceship travels at 12.0 km/s, how far does it travel in one hour? First you need to convert the hours to seconds so that the whole problem is in the same units of time. . Now we can use (after rearranging formula ):
   

   
   

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