Forces and Motion

1 day = 86,400s

1 year = 31,536,000s

Answer: 7.3 x 10^{-5} m/s^{2}

You are asked to find the average acceleration, a, and distance travelled, d.

You know:

Time, t = 678 d

Final velocity, vf = 4.3 km/s

Initial velocity, vi = 0 km/s

You need to find equations that include these known variables.

Start with the definition of acceleration fro Eqn 1.3:

But the answer needs to be in m/s^{2} so the km/s has to be multiplied by 10^{3} to convert to m/s.

And the 678 d has to be in seconds. Note that 1 d = 8.64 x 10^{4} s, so:

a = (4.3 km/s x 10^{3} m/km) / (678 d *8.64 x 10^{4} s/d)

= (4.3 x 10^{3} m/s) / (5.9 x 10^{7} s) = 7.3 x 10^{-5} m/s^{2}

This is a really low rate of acceleration but it happened every second for 678 days.

Answer: 1.3 x 10^{8} km

Now, to finish up by calculating distance, d, just remember Eqn 1.7:

d = ½at^{2} = ½ * 7.3 x 10^{-5} m/s^{2} * (5.9 x 10^{7} s)^{2}

= 1.3 x 10^{11}m = 1.3 x 10^{11}m x 10^{-3} km/m = 1.3 x 10^{8} km

Looking at this page full of math it looks hard, but once again, this was only cumbersome because of the need to change units. Physics would be easier if we in America routinely expressed units in meters and seconds. Of course, then you’d have to remember that you are 1.75 m tall and 5 x 10^{8} seconds old!

Ion drive spacecraft are OK for robotic missions, but it would be nearly impossible to carry enough food for astronauts to survive an ion-drive mission even to the Moon.

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