Confused: Is this just a badly constructed question

[Stringbags]

I have a distance/velocity/acceleration question that is either badly constructed or I am missing something.

We have a vehicle who's velocity is modeled by v= 119(1-e^-0.1408t).

we can integrate to find the formula for distance traveled giving s= 119t+(847e^-0.1408t) + c

We are given that the vehicle travels 400m in 10.5sec giving us a constant of integration of -1045

This gives us the full formula of s = 119t+(847e^-0.1408t) -1045 unless I have done something stupid.

The problem is that the exponential component has a negligible effect, effectively giving the linear equation s = 119t -1045

If we look at this in reality the intercept at s is at -1045m meaning that the vehicle has to travel for 9 seconds before it passes the start line.

If the constant of integration is given as zero the vehicle travels 1442m in 10.5 secs not 400m as given.

Any ideas?

P.S. Maximum velocity is reached in 7.1secs

[Stringbags]

Another thought is that the maximum velocity of 119m/s is reached in 7.1 seconds, therefore the final 3.4 seconds is at max speed traveling 405m, so the data given for the 400m time must be incorrect, I wonder if this is intentional to stimulate analysis?

[HallsofIvy]

I don't know what your difficulty is. Why does the fact that "the exponential component has a negligible effect, effectively giving the linear equation s = 119t -1045" bother you? You also say "the vehicle has to travel for 9 seconds before it passes the start line." What "start line" are you talking about? Are you concerned that s is NOT 0 when t= 0? Why should it be?

[Stringbags]

I'm assuming that the distance is zero when t is zero, why would I not?

[Guest]

The "distance" to what? You say "the vehicle travels 400m in 10.5 seconds" but that could be at any point along its route. It says nothing about where the vehicle started. You are assuming information not given.