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?

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.

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

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

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

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

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, 200817 yr by insane_alien

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]

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

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, 200817 yr by jedaisoul

DH just said that

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.

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

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