Originally Posted By: BRZED
Originally Posted By: javacontour
The velociraptor spots you 40m away and attacks, accelerating at 4m/s^2 to its top speed of 25 m/s. You flee, instantly reaching your top speed of 6 m/s.
How far can you get before you are devoured and how long do you have to live.
How long does the raptor need to from 0 to 25 m/s?
top speed
---------------- = 6.25 => raptor needs 6.25 seconds to reach his top speed.
acceleration
How far can I run in 6.25 seconds?
6.25 x 6 = 37.5 => I can run 37.5 meters
The raptor is 40 meters behind me whem I start running. How far am I from the raptor after 6.25 seconds of running?
40 m + 37.5 m = 77.5 => I am 77.5 m away from the raptor by the time I reach top speed. The raptor will clearly reach me before 77.5 meters, and someone else can do the rest of the calculations, which for me, who just got eaten, are irrelevant. Death took my will to do math. Also, raptors are pack hunters and very likely another one or two will cut me off. Remember great white hunter Mr. Muldoon and his famous last words? "Clever girl!"
BRZED, you're correct - After 6.25 s, the velociraptor (VR for short) hits its top speed of 25 m/s and has covered 78.125 m. And, if the VR had not been there, you (would have) covered 37.5 m. Add in the 40 m initial separation, and after 6.25 s you would have been 77.5 m away from the VR's starting position. BUT, you never made it. So, you're right, the VR's top speed is moot - he never reaches it.
So digging back several decades ...
distance between you and the VR = D, in m
D0 = your initial distance away from the VR, in m
V1 = your speed away from VR (increasing D), in m/s
V2 = VR's speed toward you (decreasing D), in m/s
A = VR's acceleration in m/s^2
T = elapsed time in seconds
So, D = D0 + V1*T - V2*T
D = D0 + V1T - 0.5*A*T^2 (V = 1/2 AT)
D = 40 m + (6 m/s * T) - 0.5(4 m/s^2)T^2
Dropping the units ...
D = 40 + 6T - 2T^2
We want to know what T is when D = 0, so ...
0 = 40 + 6T - 2T^2
2T^2 = 6T + 40
T^2 = 3T + 20
T^2 - 3T - 20 = 0
OK, if Mr XKCD were a nice guy, he would have set this up such that it would factor nicely ...
Unfortunately, it doesn't. If it did, either term could be set to zero, with one yielding a negative time which could be discarded.
Anyway, resorting to the calculator and plugging in successively closer numbers, VR would catch you after approximately 6.2175 s, shortly before he would have hit his top speed.
Oh well, it's raining this evening ... couldn't have gotten much done outside anyway!
