calculating top speed

[pworkmaster7336]

If I know the distance an object travels from point A to point B, that it starts from a stopped position and the time that it takes to get from point A to point B, how can I calculate the top speed at point B?

[ajb]

You can calculate the average speed using

 

[math] speed = \frac{distance}{time \:\:taken}[/math].

 

Without knowing any more we can't calculate things like instantaneous speed or the maximum speed.

[insane_alien]

you could assume a constant acceleration and work it out from there as it does say it started at 0 velocity.

[swansont]

If you do have constant acceleration, you would use v = at (since it started at rest)

[pworkmaster7336]

Assuming the object has constant acceleration and travels 989 feet in 27.009 seconds, what is the top speed in mph?

[Fuzzwood]

Impossible to say without knowing the acceleration. Only thing you can calculate from this is V_avg

[insane_alien]

dude, s=at^2

 

or, rearranged a=s/t^2

 

where a = acceleration

t=time

s= displacement.

 

we do know the acceleration.

Edited August 2, 2008 by insane_alien

[D H]

dude, s=at^2 or, rearranged a=s/t^2

 

Dude, you missed a factor of 1/2: [math]d=\frac 1 2 at^2[/math] (I prefer 'd' for displacement; using 's' is confusing as it is also used for speed.) Combining with [math]v=at[/math] and solving for the final velocity in terms of distance and time,

 

[math]v=at = 2\frac d t[/math]

[insane_alien]

gah. i've been doing that a lot lately. think i'll go take a nap.

[jedaisoul]

Surely, with constant acceleration, the maximum velocity is twice the average velocity (assuming you start at zero velocity)? It's a straight line graph of velocity against time. Or am I missing something?

 

989 / 27.009 = 36.6174 ft/sec ave. velocity

So Max velocity = 36.6174 * 2 = 73.235 ft/sec.

 

I'll let you do the conversion to mph.

Edited August 8, 2008 by jedaisoul

[insane_alien]

DH just said that

[jedaisoul]

DH just said that

Yes, I did not spot the significance of the last line of DH's post. But then again, I wonder whether the enquirer would have grasped the meaning of the formal proof given? My solution was less rigorous, but I hope more intelligible to a casual reader.

[Severo]

x = xo + vot + at²/2

989 = 0 + 0.t + a(27,009)²/2

989 = a(27,009)²/2

989 . 2 = a(729,486081)

1978 = a (729,486081)

a = 1978/729,486081

a = 2,7114979319255852943409347929697

 

in feet/second

just convert

 

xD

[pworkmaster7336]

:doh:Thanks for your help! I think I've got it now.