position function without a C

[sialoproject]

A car heads north from Austin on IH 35. Its
velocity t hours after leaving Austin is given
(in miles per hour) by
v(t) = 3 + 2t ? 6t

What will be the position of the car after 2
hours of driving?

I know that to find position of a function, one needs to do an integral of a V(t).
My problem is after doing that I don't know what the constant is...

V(t) = 3 +2t-6t
P(t) = 3t + t^2 - 3t^2 + ????

if i plug p(2) without C it gives me negative number...which is obviously wrong. please help

 

[Deleted member 4993]

A car heads north from Austin on IH 35. Its
velocity t hours after leaving Austin is given
(in miles per hour) by
v(t) = 3 + 2t ? 6t

What will be the position of the car after 2
hours of driving?

I know that to find position of a function, one needs to do an integral of a V(t).
My problem is after doing that I don't know what the constant is...

V(t) = 3 +2t-6t
P(t) = 3t + t^2 - 3t^2 + ????

if i plug p(2) without C it gives me negative number...which is obviously wrong. please help

Are you sure that you have posted the correct expression for v(t)?

 

[Pklarreich]

Try INTERPRETING your v(t) and P(t), as in

v(t) = speed going away from Austin at time t.
P(t) = distance away from Austin at time t.

Now just think:

Where is the car at t = 0? Dallas? Houston? Chicago?

So what is P(t) at t = 0?

Then what must be the value of C?

(Of course you fix the missing exponent, too.)

 

[sialoproject]

my bad its 6t^2...and the help from the 2nd guy, i am grateful but I still can't figure it out.

 

[Deleted member 4993]

my bad its 6t^2...and the help from the 2nd guy, i am grateful but I still can't figure it out.

redo the integration.

assume at t= 0 you have p(0) = 0

 

[Pklarreich]

I don't know why, but:

V(t) = 3 +2t-6t^2

p(t) = 3t + t^2 - 2t^3 + P0

p(0) = p0 = 0.

p(t) = 3t + t^2 - 2t^3

p(2) = 6 + 4 - 16 = - 6

Why is that so obviously wrong? Looks OK to me. I checked and found that:

A. Interstate 35 does, in fact go through Austin.
B. I 35 goes N and S.

So interpret this as 6 miles South of Austin. Nothing wrong with that.
{I have made the font bigger. My wife says I'm too timid.]