Thread: Motion equations

Hi all,
Im new to the forum .

I am writing a application that displays predicted quarter mile preformance of cars based on power and weight.
I am attempting to add a visual display of the acceleration of the car. I have been using suvat equations but for some reason i cant seem to get the desired results (maybe because the car doesnt have a constant accelerations?).

given the following data:

distance = 402m
start speed = 0
end speed = 147mph / 65.71ms
acceleration = ???
time = 10 seconds

now for some reason, whenever i put the forumula into my program(or even on paper) the distance ends up as ~700m. and the time is usually much quicker than 10seconds??!?!

Im sure it must be something i am doing wrong. see my working below:
*************************

distance = startspeed*time + 0.5*a*t^2
dis = 403 (quartermile)

.: 403 = 0.5*a*10^2
.: 403/100 = 0.5*a
.: 4.03/0.5 = a
.: a= 8.6??????

*************************

endspeed = startspeed + at
.: 147 = 0 + a*10
.:147/10 = a
.: a= 14.7ms????

*************************

endspeed^2 - startspeed^2 = 2*a*d
.: 21609 - 0 = 2*a*403
.: 21609/2 = a*403
.: 10804.5/403 = a
.: a= 26.81

*************************

SO
As you can plainly see, i am no mathamitican.
i get 3 completely different valuse for acceleration?!?!

To summerise, what i want to be able to do is get the total distance traveled at intervals of say 0.1 seconds using the data provided.
I know the car doesnt have constant acceleration but surly it can be converted into a constant accleration.

Thanks again
Neil.

Originally Posted by hopoffbaby

Hi all,
Im new to the forum .

I am writing a application that displays predicted quarter mile preformance of cars based on power and weight.
I am attempting to add a visual display of the acceleration of the car. I have been using suvat equations but for some reason i cant seem to get the desired results (maybe because the car doesnt have a constant accelerations?).

given the following data:

distance = 402m
start speed = 0
end speed = 147mph / 65.71ms
acceleration = ???
time = 10 seconds

now for some reason, whenever i put the forumula into my program(or even on paper) the distance ends up as ~700m. and the time is usually much quicker than 10seconds??!?!

Im sure it must be something i am doing wrong. see my working below:
*************************

distance = startspeed*time + 0.5*a*t^2
dis = 403 (quartermile)

.: 403 = 0.5*a*10^2
.: 403/100 = 0.5*a
.: 4.03/0.5 = a
.: a= 8.6??????

*************************

endspeed = startspeed + at
.: 147 = 0 + a*10
.:147/10 = a
.: a= 14.7ms????

*************************

endspeed^2 - startspeed^2 = 2*a*d
.: 21609 - 0 = 2*a*403
.: 21609/2 = a*403
.: 10804.5/403 = a
.: a= 26.81

*************************

SO
As you can plainly see, i am no mathamitican.
i get 3 completely different valuse for acceleration?!?!

To summerise, what i want to be able to do is get the total distance traveled at intervals of say 0.1 seconds using the data provided.
I know the car doesnt have constant acceleration but surly it can be converted into a constant accleration.

Thanks again
Neil.

You are doing nothing wrong in your calculations. I would strongly suspect that the error is in using the SUVAT equations at all. There is no reason to expect that a car will maintain a constant acceleration over the 10 second period.

What I would do is plot a graph of speed vs. time. That way you can calculate the acceleration over small time intervals. It'll be messy and involve calculus before you are done, but its doable.

-Dan

Originally Posted by hopoffbaby

...
given the following data:

distance = 402m
start speed = 0
end speed = 147mph / 65.71ms
acceleration = ???
time = 10 seconds
...
Im sure it must be something i am doing wrong. see my working below:
*************************

distance = startspeed*time + 0.5*a*t^2
dis = 403 (quartermile)

.: 403 = 0.5*a*10^2
.: 403/100 = 0.5*a
.: 4.03/0.5 = a
.: a= 8.6?????? ....... OK

*************************

endspeed = startspeed + at
.: 147 = 0 + a*10 ....... endspeed = 65.71 m/s
.:147/10 = a
.: a= 14.7ms????

*************************

endspeed^2 - startspeed^2 = 2*a*d
.: 21609 - 0 = 2*a*403
.: 21609/2 = a*403
.: 10804.5/403 = a
.: a= 26.81

*************************

...

To cover a quarter mile in 10 s you need an acceleration of 8.6 m/s².

The given data show that the car has an acceleration of a = 6.57 m/s².

So don't believe the driver - he is exaggerating as allways!