A certain sporty car claims that it does "zero to sixty (mi/h) in 6.2 s". How far has it traveled by then?
First, we need to find the accelertion.
Life will be somewhat simpler if we change the velocity to SI units of km/h or, better yet, to m/s
v = 60 mi/h [ 1.61 km/mi ] [ h/60 min ] [ min/60 s] [ 1 000 m/km ]
v = 26.8 m/s
(Hmmmm, . . . that looks familiar. We've seen it before but it's not worth memorizing).
a = (v - vi) t
a = (26.8 m/s) / (6.2 s)
a = 4.32 m/s2
Now, how far does it travel in that time?
x = xi + vi t + (1/2) a t2
x = 0 + 0 + (1/2) (4.32 m/s2)(6.2 s)2
Do a quick dimensional analysis and notice that the units are consistent.
x = 83.0 m
(c) 2000, Doug Davis; all rights reserved.