# Acceleration, velocity, distance, speed and time help please

• Rich_M
In summary, the protagonist wants to travel between two planets 100 million kilometers apart using a spacecraft that has an acceleration of 9.8 m/s/s. If he remembers correctly, he could travel for 4.9 million meters and have a final velocity of 9.8 m/s. If he wanted to travel for 50 million meters, he would need to accelerate for 1/2 the way then decelerate the rest of the way.

#### 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

Rich_M said:
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).

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.

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.

## What is acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is a vector quantity and is measured in meters per second squared (m/s^2).

## What is velocity?

Velocity is the rate at which an object's position changes over time. It is a vector quantity and is measured in meters per second (m/s).

## What is distance?

Distance is the total length of the path an object has traveled. It is a scalar quantity and is measured in meters (m).

## What is speed?

Speed is the rate at which an object covers distance. It is a scalar quantity and is measured in meters per second (m/s).

## How are time, distance, velocity, and acceleration related?

Time, distance, velocity, and acceleration are all related through the equations of motion. The equations describe the relationships between these quantities and can be used to calculate one quantity if the others are known. For example, the equation v = u + at relates velocity (v), initial velocity (u), acceleration (a), and time (t).