Calculating the speed of an object going through multiple distance & acceleration phases

[Shylo132]

Hello,

I am a Game Designer for Faceless Mirage Studio and ran into my own little problem of advanced math.

Current formula's I have been attempting to use:

a=dv/dt

Constant Acceleration Motion

hyperphysics.phy-astr.gsu.edu

Variable Acceleration Motion

hyperphysics.phy-astr.gsu.edu

Attachment is my current excel sheet, I can calculate per zone, but currently unable to calculate each zone as the initial velocity has changed and being able to apply that new initial velocity with the new multiplier. To my knowledge, each zone should be cleared faster than my current math due to the increasing speed as the object continues to accelerate, even at reduced speed through each zone.

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Current Math Problem:

Unit of measurement is meters and meters per second (m, m/s)

Spaceship starts at 0 velocity and 0 acceleration at position 0 at the very beginning of Zone A

Spaceship has default value of 10m/s acceleration (A)
There are 5 zones consisting of the following:
Zone A:
Modifies acceleration by (A*7) = 70m/s
Total Length of 750m
Zone B:
Modifies acceleration by (A*6) = 60m/s
Total Length of 1200m
Zone C:
Modifies acceleration by (A*5) = 50m/s
Total Length of 1800m
Zone D:
Modifies acceleration by (A*4) = 40m/s
Total Length of 2500m
Zone E:
Modifies acceleration by (A*3) = 30m/s
Total Length of 3000m

What is the max speed the spaceship will be when it reaches the total distance of 9250m (Sum of all zone distances) when accelerating through all 5 zones in succession.

If this is able to be solved, I then need to understand how to calculate it in reverse so I can apply this for deceleration.

I appreciate any and all help, thank you so much in advance, I will answer and learn as much as you guys let me.

 

[HallsofIvy]

I think you need to go back and check the problem statement again. What you have written makes no sense.

What does "modifies acceleration by 70 m/s" mean? 70 m/s is SPEED, not acceleration. Was it supposed to be "70 m/s^2" or "modifies speed by 70 m/s"? And is that "modification" an increase or a decrease?

 

[Shylo132]

Hello, I am sorry it is confusing because I don't really know how to organize the information in the first place.

Ship increases from 0 speed by 70m/s for 750m in zone A.

From the speed obtained from zone A, speed would then decrease to 60m/s (-10m/s) for 1200m. (A reduction in overall acceleration speed? But still increasing overall speed.)

From the speed obtained from both zone A and B, it would then decrease to 50m/s for 1800m. etc.

I hope this helps?

 

[JeffM]

Hello, I am sorry it is confusing because I don't really know how to organize the information in the first place.

Ship increases from 0 speed by 70m/s for 750m in zone A.

From the speed obtained from zone A, speed would then decrease to 60m/s (-10m/s) for 1200m. (A reduction in overall acceleration speed? But still increasing overall speed.)

From the speed obtained from both zone A and B, it would then decrease to 50m/s for 1800m. etc.

I hope this helps?

Nothing in your excel spread sheet talks about zones. I can sort of figure out what some of your formulas are from the spreadsheet, but you are dumping us into the middle of a problem and assuming we can intuit what you are trying to do.

it looks as though you are giving us an example from planet under halo. Where does the 750 come from? What are the units associated with these numbers? Where does the 10.71 come from?

And then we are in never-never land. “Overall acceleration speed” is a meaningless phrase. For speed to fall, we need a negative value for acceleration, and I see no negatives.

 

[Shylo132]

Ah, copy.

Zone A - Halo
Zone B - Espial
Zone C - Core
Zone D - Arbiter
Zone E - Graveyard

The spaceship has a default value of 10 acceleration when thrusting forward up towards a max speed, currently the max speed is set to 50k to allow testing. Each zone applies a specific multiplier that defines how strong the gravity in that zone is.

Distances are defined by myself as the length of each zone (they are orbital rings around a planet, but the player is passing straight through in a straight line through each orbit zone ")>)>)>)>)>)" ).

So for a normal Planet in "Zone A - Halo" is a 750m wide ring around the planet. It applies a x7 multiplier to player acceleration. Once the player has reached "Zone B - Espial" they are still traveling at whatever speed they obtained from Zone A but now at a different acceleration and continuing to speed up as they head into "Zone C - Core"

So the ship should start at 0, obtain a speed at an increasing speed of 70m/s acceleration for a certain distance, at zone b they should have a speed obtained by zone A that is then stacked upon across zone B, etc.