# How to calculate the deceleration of the object

• Moon54
In summary, the deceleration of an object is a function of the final velocity and the time between the start and end of the motion.

#### Moon54

Hi, i am trying to understand, how to calculate the deceleration of the object?
I have a small toy car in the track, after i release the car, i want to calculate the deceleration of the car, and predict how many loops, it's going to do, after measuring the timing of some revolutions. Is there any deceleration formula or something like that?

Ps. Sorry for my english, i am not from USA.

You need to know what forces are acting on it to decelerate it. In this case it will be friction and air resistance

If you can measure the speed of the car at two points and the time it takes to go between them you can calculate the deceleration.

OK, i will try to do it. I get one problem, the deceleration, has to increase every time, or once i run the object, it's constants?
Let's say, for example, the deceleration is 1cm/s, it has to increase, or from start to the end, it will be 1cm/s?

That depends on what causes the deceleration. If it's air resistance then the drag force isn't constant so the deceleration isn't constant.

If it's friction in wheel bearings it might be constant.

Moon54 said:
Let's say, for example, the deceleration is 1cm/s, it has to increase, or from start to the end, it will be 1cm/s?

You mention the car doing “loops” which I assume means the car is going around a track. If the track has straight sections and curved sections the resistance will certainly be different in those regions.

Is this homework ?

I'm new here and not sure what level you are coming to this from. I assume it's some kind of wind-up toy car or there is some way to change the release speed. If it’s a wind-up, it may accelerate after release before it starts slowing again. Aero drag is D= ½ p V^2 S Cd so D force will be greatest at the highest speed. Rolling resistance is a constant though.
D = Drag Force
p = density of fluid (from memory) 1.225 kg/m^3 air at sea level.
S = Frontal surface area
Cd = coefficient of drag

Sounds like there could be a lot of things to account for and many unknowns. It might be simpler to do the coast down tests and record results in Excel, you can then use excels regression tools to produce a mathematical model for the deceleration in relation to starting energy/speed etc. The accuracy of results will depend on the regression curve type you use. Try different curves and pick the one that gives the best correlation coefficient. It won’t be physics formulae but it will be a practical predictive model.

If you don’t understand what I am saying, I am aiming my answer at too high a level (not sure how that works yet) so apologies.

I get the timings, but if i try to calculate the deceleration, everything looks so random... Something is not working.

All i do, is: endingVelocity - begingVelocity / << What time put here? Should be 1000ms, or the last endingVelocity, from the last revolution?

Can you describe the motion of the car. Is it going round a loop (vertical circle)?

Can you make a photo of the track?

Not really, but if i do multiple tests, i get something like average deceleration, and this one has accetable accuracy, but i want to know, if there is a better way.

No, it's horizontal movement, clockwise.

One problem is knowing if the deceleration is constant or variable and how it varies. The equation

a = (V - U)/t

Where U is the initial and V the final velocity, Is really only useful if the deceleration is constant.

One possibility would be to video it and look at the distance moved between frames to calculate the velocity. Plot velocity against time. The acceleration is the slope of the line, which might vary.

Moon54 said:
Let's say, for example, the deceleration is 1cm/s, it has to increase, or from start to the end, it will be 1cm/s?

do you understand that acceleration (or deceleration) has units cm/sec/sec, not cm/sec?

It is the rate at which an object slows down. Deceleration is the final velocity minus the initial velocity, with a negative sign in the result because the velocity is dropping. The formula for acceleration can be used, recognizing that the final result must have a negative sign.

wahidovic123 said:
it is the rate at which an object slows down.
Yes
deceleration is final velocity minus the initial velocity
This is only half the story, you also need to know the time between initial and final speed measurements. Acceleration is the change in speed divided by the time it took to change;
delta V / delta t

Moon54 said:
I have a small toy car in the track, after i release the car, i want to calculate the deceleration of the car, and predict how many loops, it's going to do, after measuring the timing of some revolutions. Is there any deceleration formula or something like that?

Ps. Sorry for my english, i am not from USA.

It may be a problem with English. Your question makes no sense using "deceleration". That is confusing the answers. Do you mean "speed"?

I have a small toy car in the track, after i release the car, i want to calculate the speed of the car, and predict how many loops, it's going to do, after measuring the timing of some revolutions. Is there any speed formula or something like that?

The whole problem is how to "guess" or calculate the deceleration, if it's not constant. I am sure, there is a various range, and it changes only a little. That's my biggest issue, because i want to do some different test's, and i would like to know if there is any formu
for that.

I can only suggest using video to measure how the speed changes. Put the data into Excel and do some curve fitting.