Acceleration, velocity, distance, speed and time help please

[Rich_M]

Hi Everyone,
This might be a little too complex for me to understand the answer, But here goes:

1) I have a fictional spacecraft , frictonless and an infinite supply of fuel.

2) It is able to accelerate at 9.8 m/s/s.

3) I want to travel between 2 planets 100 million kilometers apart.

4) I want to accelerate 1/2 way then deccelerate the rest of the way.

I know:

distance = 100,000,000km = 100,000,000,000m
acceleration = 9.8m/s/s
time = ? in seconds
velocity = 9.8*time = ?m/s

I can break the trip in two 50,000,000,000m if I figure the time and max velocity for the acceleration phase, I know it for the deceleration phase.

if I remember right (high school physics was 30 years ago) I would travel
4.9m, ending with a velocity of 9.8m/s after the first second.
9.8m, (total 14.7m), ending with a velocity of 19.6m/s after the second second.
19.6m, (total 34.3m), ending with a velocity of 29.4m/s after the third second.

I know I could use a spread sheet and just keep doubling the distance, adding it to the total distance and add another 9.8m/s to the velocity until I got to 50,000,000,000m, But there must be a formula to figure this out, my question is where can I find the formula.
Thanks
Rich

 

[hage567]

If you want to try to figure it out yourself, you can look here at the "Basic equations of 1-d kinematics" https://www.physicsforums.com/showthread.php?t=110015

 

[nrqed]

Hi Everyone,
This might be a little too complex for me to understand the answer, But here goes:

1) I have a fictional spacecraft , frictonless and an infinite supply of fuel.

2) It is able to accelerate at 9.8 m/s/s.

3) I want to travel between 2 planets 100 million kilometers apart.

4) I want to accelerate 1/2 way then deccelerate the rest of the way.

I know:

distance = 100,000,000km = 100,000,000,000m
acceleration = 9.8m/s/s
time = ? in seconds
velocity = 9.8*time = ?m/s

I can break the trip in two 50,000,000,000m if I figure the time and max velocity for the acceleration phase, I know it for the deceleration phase.

if I remember right (high school physics was 30 years ago) I would travel
4.9m, ending with a velocity of 9.8m/s after the first second.
9.8m, (total 14.7m), ending with a velocity of 19.6m/s after the second second.
19.6m, (total 34.3m), ending with a velocity of 29.4m/s after the third second.

I know I could use a spread sheet and just keep doubling the distance, adding it to the total distance and add another 9.8m/s to the velocity until I got to 50,000,000,000m, But there must be a formula to figure this out, my question is where can I find the formula.
Thanks
Rich

This calculation would require the use of special relativity. Do you kno wsome special relativity? (if you use the non-relativistic kinematic equations with an acceleration of 9.8 m/s^2, you will end up having a spacecraft moving faster than the speed of light, which is unphysical).

 

[hage567]

Yeah I guess it does. I didn't look at the numbers that closely. You can find relativistic equations of motion in the same thread I posted earlier I think.

 

[Rich_M]

Space to work out this problem.

I'll try to work this out, It might take a while though.

Things I know:
c = 299,792,458m/s
c^2 = 89,875,517,873,681,800m/s
a = 9.8m/s/s



Things I might have to work out:

$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

My Brain Hurts, this as far as I go tonight, I'll try again tomorrow.