One day it started snowing at a heavy and steady rate. A snowplow started out at noon, going 2 miles the first hour and 1 mile the second hour. What time did it start snowing?
I know the answer to this problem and how it is usually approached. But I was wondering if there was another way to solve it.
If c1 equals the change in acceleration due to increasing resistance from the snow then I get the following four equations:
d3x/dt3 = c1
d2x/dt2 = c1t + c2
dx/dt = (1/2)c1t2 + c2t + c3
x = (1/6)c1t3 + (1/2)c2t2 + c3t + c4
Where (0,0),(1,2),(2,3) .
The problem is I don't have enough points to solve for c1 and c2, which I think are the only two constants I need so that I can set acceleration equal to zero and solve that equation. Is there something I am missing here, or am I way off the mark?