Okay, megan24. You WILL have to do better than that.
Let's catalog what we know...
"As John drives past 3 lamp posts, each 30 m apart, on a road with speed limit of 30 miles per hour, the traffic police registered the time taken for him to travel between the posts. The equipment registered 3 seconds to travel from lamp post 1 to lamp post 2.. and he took 2.2 seconds to travel from lamp post 2 to lamp post 3. Set up a model to determine whether John had broken the speed limit as he drove past the middle lamp post."
There are three lamp posts. You already called them Post 1, Post 2, and Post 3.
At Post 1 (Time = 0), John has SOME speed. We just don't know what it was. Let's call it V1. (vee-one)
Let's also start a linear coordinate system and call Post 1 the starting point. x = 0 m
At Post 2 (Time = 3), John has SOME speed. We just don't know what it was. Let's call it V2. (vee-two)
We've moved to Post 2, so x = 30 m
At Post 3 (Time = 5.2), John has SOME speed. We just don't know what it was. Let's call it V3. (vee-two)
Now, we're at Post 3, so x = 60 m
It's easy enough to calculate and average speed for the whole trip. (60 m)/(5.2 sec) Done. Convert that to mph and see how close to 30 mph you get. It's just an exploration exercise. It does not answer the question.
The last piece of information we need to glean from the problem statement is that the trip from Post 1 to Post 2 took more time than the trip from Post 2 to Post 3. This suggests to the mind that John was ACCELERATING! For the sake of simplicity, let's assume it was uniform Acceleration.
Right now, I'm tempted to calcluate the average speed of both pieces. (30 m)/(3 sec) and (30 m)/(2.2 sec). Does either of those suggest that the speed limit was broken? Again, just an exploration exercise. This also fails to answer the question.
Finally, you should have in your bag of tricks a trio of formulas for Uniform Acceleration.
Acceleration: A(t) = a -- Acceleration is constant.
Velocity: V(t) = a*t + V0 -- The velocity is whatever we started with increased by whatever acceleration we have experienced.
Displacement or Location: X(t) = ½*a*t^2 + V0*t + X0 -- This one is a little harder to explain in words. Suffice it to say that where we are is the sum of where we started, increased by some velocity and aceleration components.
What I wish you had told me is if we get to use any Calculus. If we DO, then it is easy enough to explain the relationships between these three function defintions. If we do NOT, you'll just have to remember them for now.
Okay! That was half a chapter. Let's see if you can put all the pieces together and get a reasonable answer.
I dont know how to prove this and having a hard time with this question!