Optimization Problem: What value of 'a' would enable the car

[zutrough]

Hi, this is my first post...I'm just having a little trouble with an optimization word problem.

A car starts from rest and travels with constant acceleration at "a" ft/s^2. What value of "a" would enable the car to travel 300 ft in 5 seconds?

My only real problem is figuring out what equation to use, in order to associate all the variables with one another. I've seen V(sub T) = V(knot) + at ... and I've also seen x = 1/2 at^2 + v(knot)t + x(knot). Both of these use "a" as the constant acceleration, but I am confused as to which one I should use to get the solving started. I would greatly appreciate your help.

 

[tkhunny]

First off, it's "naught" or "nought", not "knot", but that's not all that important.

You should know the basic definitions:

Position or Location

s(t) = (a/2)*t^2 + v*t + h

Velocity

v(t) = s'(t) = a*t + v

Acceleration

a(t) = v'(t) = s"(t) = a

h is initial position, zero (0) in this case
v is initial velocity, zero (0) in this case
a is constant acceleration.

You are given a(t) = a

You need s(5) = 300

How are you going to get there?

 

[zutrough]

Alright, since s(t)=(a/2)t^2+vt+h contains all variables, I decided to use it to begin with. S(5)=300, so 300=(a/2)5^2+0+0; 300=(25a/2); 600=25a; a=24

So I've found "a"...is this the end? It seemed incredibly too easy, so I'm sure I messed something up.

Thanks for the help and the clarification on the spelling of "naught."

 

[tkhunny]

I suppose it could use some units, but why else don't you like it?

Many problems are designed to test definitions. It apears you can calculate just fine. You did not come up with the definition. Work on that part.