Question

Acceleration Formula

Asked by: OBCT

I know very little about maths and physics but I need a formula for a car accelerating.
This is going to be used in a very basic program that I am writing.
These are the variables that will have to be in the forumla.
-Car weight
-Distance
-Time
-Speed

A random number between 14-15 (for example) will be generated by my program, then set as "t".
The car weight will be "w", distance "d" and speed as "s"

The formula should calculate the current speed as it starts from 0, then accelerates at an even pace to drive straight while driving "d" and finishes at the exact time specified by "t".
As I said, I no very very little about this area so I'm not even 100% sure what I'm actually trying to do. Please bare with me.
Cheers

-OBCT

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Asked On
2003-12-26 at 07:19:20ID20834909
Tags

acceleration

,

formula

Topic

Math & Science

Participating Experts
5
Points
500
Comments
13

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Answers

 

by: dhyaneshPosted on 2003-12-26 at 08:06:34ID: 10002333

Hi OBCT,

First of all car weight will not affect the acceleration or speed.

There are 3 basic kinematic equations which are used to solve problems like this. (You might need only one)

v = u + a*t

d = ut + 0.5*a*t*t

v*v = u*u + 2*a*d

where

u - initial speed
v - final speed
a - accleration
t - time
d - distance

From second equation:

In your case initial speed = 0 hence u = 0. Therefore second equation becomes

d = 0.5*a*t*t

Hence  a = d/(0.5*t*t) which is your required acceleration.

Then once acceleration is fixed speed at any time 't' can be found from first formula (again u = 0)

v = a*t

Weight will come into picture only if you have the driving force of the car. Then acceleration would be :

a = Force / Mass

Dhyanesh

 

by: OBCTPosted on 2003-12-26 at 08:19:43ID: 10002392

Dhyanesh,

Thank you for your response and great explination.

Just a few questions:
1) How do I set the acceleration when I am not sure what it be?
2) What is distance mesured in?

Cheers

-OBCT

 

by: GwynforWebPosted on 2003-12-26 at 11:10:33ID: 10002974

OBCT,
 I read this

 'starts from 0, then accelerates at an even pace to drive straight while driving "d" and finishes at the exact time specified by "t" '

as starting from 0 and accelarating at a constant rate until a disatnce d has been travelled been travelled in a time t.

Starting with a speed 0 then a time T the speed V is and the distance travelled D at any given time T is

V = a*T

D = 0.5aT²

however as I read you want to know what is the accelaration required to travel a distance d in a given time t ie find a such that

     d = 0.5at²

which gives

  a=2*d/t²

this may or may not be what you are looking for.

The dimensions of the accelaration, distance  and time can be what ever you want but must be constistent eg

d=miles  t=hours     v= miles per hour   a=miles per hour per hour

or

d=feet   t= seconds  v=feet per second   a=ft per second  per second

GfW

 

by: dhyaneshPosted on 2003-12-26 at 21:15:57ID: 10004367

OBCT,

You can set the acceleration as I have put in my above post as:

a = d / (0.5*t*t)

which is the same as what GwynforWeb  has posted.

Another way would be

a = Driving Force of Car / Mass of Car

However then you can keep either 'd' or 't' fixed and find the other. In other words once acceleration is fixed then you can ask for 'd' and calculate 't' or vice-versa.

Dhyanesh

 

by: OBCTPosted on 2003-12-30 at 05:38:58ID: 10015999

I just have one more question that I think I'll need to know...
How can I simplify 'a' (being miles per hour per hour)
It's probably a very simple thing to figure out however maths is definatly not my strong point.

Thanks for all your help :)

Cheers

-OBCT

 

by: dhyaneshPosted on 2003-12-30 at 08:07:08ID: 10016709

OBCT,

I did not get your question. Acceleration 'a' will be miles per hour per hour OR miles per hour square. The units can not be simplified further. What do you want to simplify?

Dhyanesh

 

by: OBCTPosted on 2003-12-30 at 19:06:27ID: 10019771

How can I convert the mesurments to the metric system (I live in Aus)
So
d = kilometers, v = kilmeters per hour, a = kilometers per hour per hour

 

by: ozoPosted on 2003-12-30 at 19:12:18ID: 10019785

A mile is 1609.344 meters

 

by: OBCTPosted on 2003-12-31 at 00:23:53ID: 10020650

I tried using the formula for the first time (I couldn't before because of programming that had to be done) and I am not sure if I got the correct answer.
I used this:
a = d / (0.5*t*t)    
which became    
a = .4 / (0.5 * 10 * 10)        // .4 is 400 meters & 10 is 10 seconds
The answer I got was = 8x10 -3
I have no idea what that means or how to use it.

 

by: ozoPosted on 2003-12-31 at 00:43:17ID: 10020672

.008 kilometers per second squared = 8 meters/sec/sec = 28.8 km/hour/sec = 103680km/hour/hour

 

by: tapankhatriPosted on 2004-01-26 at 05:43:44ID: 10200576

Dear Mr. OBCT,
You kno what is acceleration it is the rate of change of speed. If a car is running at speed of 150 km/hr (constant) its acceleration is zero! Yes its zero. If you say that car reaches speed of 60 mts/sec in 1 second then the acceleration of car is 60 mtr/sec2 (second square). The formula for acceleration is a = speed / time. Weight of car will not play any role where as the speed and time will help you out. (Subs titute in above formula)

so,

acceleration = speed / time

Take speed in mts/sec, time in sec (you will get exact acceleration)

(u take speed in mts/sec & time in sec)
(1000 mts = 1 Km)
(1 mile = 1.6 km)
(1 minute = 60 sec)
(1 hour = 3600 sec)

Ps.: mts = meters, Km = kilo meters, sec = seconds

 

by: OBCTPosted on 2004-01-26 at 05:56:52ID: 10200668

I would like to appologize to everyone for leaving this question open for so long. I havn't had a chance to really sit down and work some things out but I'm sure I'll have no problems now that I have all these formula's.
Thank you all for your help :)

Cheers

-OBCT

 

by: LengorePosted on 2004-02-13 at 06:18:06ID: 10352309

A bit late in the day - haven't looked at this section for a while.

dhyanesh gave Newton's equations in the first reply - these of course apply only for a constant rate of acceleration which is what you specified.

Any units can be used provided they are consistent, for example if the distance is in metres and the time in seconds then the speed must be metres/second and the acceleration in metres/second/second.

As everyone has said, weight doesn't come into these calculations.  However, weight (or more correctly, mass) does determine how much force is needed to produce a given rate of acceleration.  (Isaac Newton again, Force = Mass times Acceleration).

20120131-EE-VQP-002

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