A spaceship accelerates at a constant rate of 10 m / s^{2} for the first half of the trip and then slowing down at the same rate for the second half of the trip. The distance between Earth and Pluto is 4.773 * 10^{12} m. Can you calculate how long does it take to get to Pluto?

###### Solution.

We will use equation of the motion in a straight line

X = Xo + Vo * t + 0.5 * a * t^{2}

where Xo – the initial position of the object, Vo – the initial velocity, a – the acceleration and t – the time it takes the object to move.

We could consider that Xo = 0 and Vo = 0.

Thereby,

X = 0.5 * a * t^{2} or

t = √(2*X/a)

The spaceship accelerates half of the trip, so X will be equal to

4.773 * 10^{12} / 2 = 2.3865 * 10^{12} m.

Substitute the values of X and a into the equation

t = √(2 * 2.3865 * 10^{12} / 10)

Hence,

t = 6.91 * 10^{5} s

and the total time of the trip will be

6.91 * 10^{5} * 2 = 1.38 * 10^{6} s or 16 days.

Of course, there is more, a lot more, to space travel than just speeding up and slowing down. We have to keep track of gravitational forces, fuel supply and other things that make a 16 days trip to Pluto impossible, at least for now.