Finding time to take a trip to Proxima Centauri

[Raziel2701]

Homework Statement

find the time it would take for a one-way trip from Earth to Proxima Centauri (4.10E13 km) . Assume that the spacecraft starts from rest, travels along a straight line, accelerates halfway at 1 g, flips around, and decelerates at 1 g for the rest of the trip.

Homework Equations

$$\Delta x = \frac{1}{2} a t^2$$

The Attempt at a Solution

So I converted the distance to meters(4.10E16m) divided by two (2.05E16m) and plugged that into the equation above, as well as 9.8m/s/s for the acceleration and solved for time. Obtaining 2.05 years. So that corresponds to the first half of the trip. I then multiplied that time by two to obtain the full trip and got 4.1 years.

The answer is supposed to be 5.8 years. No relativistic effects are taken in consideration, this is an intro level physics class and I can't get the right answer when it seems to me that I'm doing the correct steps. What am I not seeing?

Thanks.

 

[phyzguy]

Using your method, I got the same answer as you did. Are you sure you are supposed to do it non-relativistically? 5.8 years is about the right answer for a proper relativistic calculation?

 

[Raziel2701]

I highly doubt we are to take relativistic effects into account. Even so, I don't know how to use the time dilation equation since the ship is not traveling at a constant velocity but a constant acceleration.

We are barely scratching the breadth of the kinematic equations in class, special relativity is not covered.

Any other ideas?