Originally posted by: RESmonkey
Wouldn't dividing 163 by 3600 only give you some sort of average of 7 seconds in the 7 hours instead of the precise 7 second distance?
No, if you want to be consistent you can convert everything from mph to mps, but then the constant factor of 3600 can be taken out of the integral
assume that t is in seconds
v(t) = 1.25mph*t^2 + 3 mph
v(t) = 1.25/3600mps*t^2 + 3/3600mps
x(t) = ? v(t) dt
x(t) = ? 1.25/3600mps*t^2 + 3/3600mps dt
x(t) = (1/3600) * ? 1.25mps*t^2 + 3mps dt
x(t) = (1/3600) * ((5/12*t^3 + 3*t)|[7,0])
x(t) = (1/3600) * 163.92