Thread: Math question for you numbers people

It's a system of equations.

The car only travels 14.67' in 2 seconds.

The bike would be accelerating hard to go 45' in that same time.

African or European Swallow?

22.46MPH, I think.

Let me go through and verify I didn't miss something.

Are the vehicles on a treadmill?

Originally Posted by ND4SPD

Are the vehicles on a treadmill?

No they are on a standard road, in normal conditions.

Originally Posted by luvtolean

22.46MPH, I think.

Let me go through and verify I didn't miss something.

Okay.

Originally Posted by luvtolean

It's a system of equations.

The car only travels 14.67' in 2 seconds.

The bike would be accelerating hard to go 45' in that same time.

Thanks. What would the acceleration be to acheive this? (also keep in mind the bike at the start of the equation was traveling 8 mph, so he was closing on the car, but clearly must accelerate to cover the distance in 2 seconds.

Speed is correct, 22.46MPH.

Acceleration is 10.6 ft/second^2

That isn't wheel off the ground fast....he picks up ~14MPH in 2 seconds...wide open on a liter bike you can pick up 60MPH in 3 seconds.

That isn't as hard as I originally thought...shouldn't post in real time when doing math problems.

Originally Posted by luvtolean

Speed is correct, 22.46MPH.

Acceleration is 10.6 ft/second^2

Thanks. What is the (roughly) top acceleration of a modern 600 cc bike?

And what does the series of equations look like L2L to solve these questions of mine?

PM me your e-mail, I'll write it up in word.

No idea what 0-60 on a modern 600 is, you'll have to find a review. Best would be a roll on test as they usually do 5-60.

What's my consultant's fee? (J/K)

Originally Posted by luvtolean

PM me your e-mail, I'll write it up in word.

No idea what 0-60 on a modern 600 is, you'll have to find a review. Best would be a roll on test as they usually do 5-60.

What's my consultant's fee? (J/K)

A big thank you, and my go-2-guy for numbers in the future.

Originally Posted by MotoVegas

A big thank you, and my go-2-guy for numbers in the future.

LTL is the man, although we have a genuine savant on this forum. Can't tell time and has questionable choices for friends , but I understand his math is pretty solid . . . .

Originally Posted by abtech

LTL is the man, although we have a genuine savant on this forum. Can't tell time and has questionable choices for friends , but I understand his math is pretty solid . . . .

Definitely no savant here!

I can't do symbols or subscripts but real quick, here's how I did it. If anyone sees errors, correct me.


V= Velocity
U= position
T= time
A= acceleration
delta T = 2 seconds


Convert to ft/s:
Vcar = 5 Mi/hr*(5280ft/1mi)*(1 hr/3600s)= 7.33 ft/s
V0_bike = 8 Mi/hr*(5280ft/1mi)*(1 hr/3600s)= 11.73 ft/s

Solve for distance car travels in 2 seconds:
delta Ucar = Vcar* delta T = 7.33*2 = 14.67ft

Solve for distance bike travels in 2 seconds:
delta Ubike = deltaUcar + 30feet = 44.67ft

Solve for average Velocity of bike:
delta Ubike = delta T * Vavg_bike
44.67 = 2 * Vavg_bike = 22.34 ft/s

Solve for Vbike @ impact, where V0_bike = 11.73 ft/s (V0_bike is the original velocity of the bike)
Vbike = 2*Vavg_bike - V0_bike
Vbike = 2*22.34-11.73 = 32.94 ft/s

Convert to MPH
32.94ft/s*(3600s/1hr)*(1 mi/5280ft) = 22.46MPH

Acceleration
a = (vbike-v0_bike)/delta T
a = (32.94-11.73)/2 = 10.60 ft/s^2

It's been a little while since I've had to do anything like that but it all looks solid to me.

0-60 times of a 600 aren't that far off from a liter bike. I think I've seen sub 3 seconds quoted in mags. 5-60mph "street start" actually slows them a bit usually due to the inability to truly "launch" the bike. The added torque of a liter bike helps make the 5-60 time faster though in comparison to the difference of a 0-60 comparison.

very good

Originally Posted by slickwill

It's been a little while since I've had to do anything like that but it all looks solid to me.

First semester physics was...that was a while ago for me!

MV, the key assumption here is that the bike accelerated at an even rate, which isn't a bad assumption at a speed that low.

Without a significant amount of data related to specific real world factors, that's as good an approximation as I can give you. Aero drag isn't a big deal at 20MPH, so that's out, and I doubt a 600 is even really getting into the sweet spot of the cams at that low a speed in 1st gear, so the engine characteristic probably isn't changing all that much, we don't however know how the rider was rolling it on and feeding the clutch.

Originally Posted by luvtolean

MV, the key assumption here is that the bike accelerated at an even rate, which isn't a bad assumption at a speed that low.

Without a significant amount of data related to specific real world factors, that's as good an approximation as I can give you. Aero drag isn't a big deal at 20MPH, so that's out, and I doubt a 600 is even really getting into the sweet spot of the cams at that low a speed in 1st gear, so the engine characteristic probably isn't changing all that much, we don't however know how the rider was rolling it on and feeding the clutch.

I can tell you my 600 sure wasn't hitting any sweet spot at those speeds. The shift to second came at 72mph. The rate of accelleration was a completely different league at 55 than at 35.

Originally Posted by Shenders1

...20-years-ago Newtonian Physics to do it in my head - I'd need to dig the book out.

I had a tough physics prof, I was afraid he'd come find me and kick my ass if I couldn't do that problem in 5 minutes.

Books are so, mid 90's physics. We have the internet now.

I converted units, then started with accel = change in velocity over time, velocity is change in position over time, derived the first equation, solved distance the car traveled, then got lazy and then did a 1 second web search so I could just choose my equations without deriving them.

Try it though, it'd take you 15-20 minutes, but I bet you could still do it.