Post: #1

You're driving your car at 90 mph on a 75mph limited road. You pass a cop car, sitting at rest.

Dodge charger, a typical cop car here in the states, gets to 60 mph in 5.2 seconds.
The cop has to
1) react
2) exceed 90 mph speed to catch you.

How much time do you have before he gets to you?

WIA

Post: #2

(03-26-2015 03:46 PM)WestIndianArchie Wrote:  You're driving your car at 90 mph on a 75mph limited road. You pass a cop car, sitting at rest.

Dodge charger, a typical cop car here in the states, gets to 60 mph in 5.2 seconds.
The cop has to
1) react
2) exceed 90 mph speed to catch you.

How much time do you have before he gets to you?

WIA

I'm no physicist but there are some missing variables here. We need to know how fast the cop is willing to drive to catch you, and once you have that number, how long does it take for a Dodge Charger to achieve that velocity.

Post: #3

I would answer this since I just completed physics 2 but I know I know I'll be pissed off if I do the calculations and someone else answers it before me, so I'll wait a few hours. And if no bites, I'll answer it.

Post: #4

It's fairly straightforward but you need to make some assumptions. 1) how long before the cop steps on the gas, and 2) a function for the acceleration of the cop car (dV/dt). The simplest way would be to assume it's linear (not realistic, but for argument's sake) and so if it's 5.2 sec to 60mph then it's 10.4 sec to 120 mph, etc. I would probably solve for the distance at which the cop reaches you and then use your constant speed to calculate the time.

Post: #5

I get 75 seconds, assuming that acceleration to 120 is 11 seconds.

The equation set up is what in wondering.

V*t + 1/2*a*t^2 = distance

Velocity, acceleration, time..

There's some unit changes cause of how things are reported.

I'm rusty though


WIA

Post: #6

15 over? may as well pull over and take the loss.

Post: #7

(03-26-2015 04:15 PM)WestIndianArchie Wrote:  I get 75 seconds, assuming that acceleration to 120 is 11 seconds.

The equation set up is what in wondering.

V*t + 1/2*a*t^2 = distance

Velocity, acceleration, time..

There's some unit changes cause of how things are reported.

I'm rusty though


WIA

Post: #8

On a related note, I 'ran' from the cops in a similar situation. Only I was doing 135mph in a 70mph zone on an FJR1300. The cop was sitting parked on the cross-thru in between the interstate lanes and I wouldn't have even seen him if he hadn't lit me up right before I passed. A quick jaunt up to 155 till the next exit, and I never saw him.

Post: #9

(03-26-2015 03:46 PM)WestIndianArchie Wrote:  You're driving your car at 90 mph on a 75mph limited road. You pass a cop car, sitting at rest.

Dodge charger, a typical cop car here in the states, gets to 60 mph in 5.2 seconds.
The cop has to
1) react
2) exceed 90 mph speed to catch you.

How much time do you have before he gets to you?

WIA

You don't know the cop's reaction time. And the cop may be parked perpendicular to the road(as they often are when hiding behind overpasses) so actually has to pull out onto the road first then turn in your direction before accelerating. That could take a few seconds. Then there's no indication of what speed he accelerates to that's faster than 90mph when catching up to you.

Post: #10

I can't tell by the responses whether or not I'm talking to STEM majors or not.

WIA

Post: #11

Ok, here are the assumptions I made:

1. The road is just an infinite straight road
2. The cop is just sitting there chillin already faced in the right direction in the shoulder, as opposed to parked perpendicularly to the road, and starts reacting the instant you drive by him
3. The cop takes 1 second to react
4. The cop drives at 100mph

I dug up that the Charger takes 14.7 seconds to get from 0-100. Add one second for the reaction time, and that is 15.7 seconds from the time you pass the cop at 90mph to the time the cop gets to 100mph. In that time, you're able to drive 631.6 meters. After 15.7 seconds, the officer has driven 328.4 meters. The difference between 100mph and 90mph works out to roughly 4.7 meters/second, so it would take the officer 64.5 seconds to close the gap once he gets to 100mph.

Post: #12

Thanks Dismal, very much along the lines.I was thinking

WIA

Post: #13

WIA, I majored in Physics but Its obvious there are a lot of other introverted scientist/engineer types on this board.

Post: #14

(03-26-2015 05:00 PM)RexImperator Wrote:  WIA, I majored in Physics but Its obvious there are a lot of other introverted scientist/engineer types on this board.

Its not introversion.that I was referring to.

WIA

Post: #15

(03-26-2015 03:46 PM)WestIndianArchie Wrote:  You're driving your car at 90 mph on a 75mph limited road. You pass a cop car, sitting at rest.

Dodge charger, a typical cop car here in the states, gets to 60 mph in 5.2 seconds.
The cop has to
1) react
2) exceed 90 mph speed to catch you.

How much time do you have before he gets to you?

WIA

(03-26-2015 04:15 PM)WestIndianArchie Wrote:  I get 75 seconds, assuming that acceleration to 120 is 11 seconds.

The equation set up is what in wondering.

V*t + 1/2*a*t^2 = distance

Velocity, acceleration, time..

There's some unit changes cause of how things are reported.

I'm rusty though


WIA

There are too many things that are not considered in that equation, the most important one is that acceleration doesnt change (this doesnt happen outside of an idealized situation), the acceleration would be greater in the beginning when hes pressing the pedal to the bottom and when there is pretty much not resistance cause by the wind, which would considerable at more than 60 mph.

To solve this in an idealized scenario you would have to make the position of each vehicle equal based on the same reference system.
Meaning for vehicle 1 the position x would be x= xo + v.t, v being 90 mph considered constant. xo would be the advantage he took since he passed the cop.
For vehicle 2 it would be x=1/2.a.t^2 since it doesnt have initial speed and youre considering your system of reference as the starting point for the cop.
You could get the accelearation by the assumed speed of 60 mph in 5.2 s
That would be v=a.t then a=60mp.3600s/5.2s.

Post: #16

WIA, have you ever been to https://www.physicsforums.com/ ?

They answer questions like this all day.

Post: #17

(03-26-2015 05:06 PM)WestIndianArchie Wrote:  

(03-26-2015 05:00 PM)RexImperator Wrote:  WIA, I majored in Physics but Its obvious there are a lot of other introverted scientist/engineer types on this board.

Its not introversion.that I was referring to.

WIA

I know. That wasn't relevant in my part. I probably just had the Meyers-Briggs thread stuck in my mind. I would hazard to guess that INTP/INTJ types make up a lot of Scientists and Engineers.

Post: #18

(03-26-2015 04:41 PM)WestIndianArchie Wrote:  I can't tell by the responses whether or not I'm talking to STEM majors or not.

WIA

I haven't studied Physics since my high school class (I did well) but this is pretty basic math...

...if you're male.

But seriously, any guy of average intelligence has an innate understanding that we use the formula for velocity every single day when we talk about speed.

Miles (or Kilometers) Per Hour is the exact same thing as saying v=d/t

I'd say most guys would understand that.

Most women, on the other hand...

Post: #19

Did a cop give you the "I had to drive at 100mph to catch you, therefore you were doing 100mph" line WIA?

Post: #20

(03-26-2015 07:38 PM)Veloce Wrote:  

(03-26-2015 04:41 PM)WestIndianArchie Wrote:  I can't tell by the responses whether or not I'm talking to STEM majors or not.

WIA

I haven't studied Physics since my high school class (I did well) but this is pretty basic math...

...if you're male.

But seriously, any guy of average intelligence has an innate understanding that we use the formula for velocity every single day when we talk about speed.

Miles (or Kilometers) Per Hour is the exact same thing as saying v=d/t

I'd say most guys would understand that.

Most women, on the other hand...

Intelligence in men is inherited mostly through the mother. If those two have a son, he's doomed. Never procreate with a dumb woman.

Post: #21

If two trains 200km apart are travelling toward each other at 50km/hr and a fly starting out in front of one of them flies to the other train at 75km/hr, and goes back and forth between the trains at the same speed whenever it hits one of them, how far does the fly travel before it gets sandwiched between the two trains?

Post: #22

No idea but, when he catches me I'm going to get a speech about how I should know better since I'm a medic (in spite of the fact that I regularly have driven rigs faster than this at work) before he lets me off with a warning.

Post: #23

(03-26-2015 08:25 PM)speakeasy Wrote:  Intelligence in men is inherited mostly through the mother. If those two have a son, he's doomed. Never procreate with a dumb woman.

I guess that explains why my dad is smarter than I.

Nonetheless, I am not sure if the intelligence of the mother is the most important factor in determining the intelligence in men. For example, one of my close friends has a brother that is smarter than him. Yet, they both have the same mother. Surely, there must be more factors in determining the intelligence in men.

Nevertheless, the theory you posted is an interesting one. Thanks for sharing.

Post: #24

1. You don't know the reaction time of the cop.
2. You don't know if his car accelerates at a constant rate.
3. You don't know how far over 90 he will drive to catch you.

v*t + .5at^2 gets you his displacement until he stops accelerating, but the v*t is irrelevant because he's starting from rest, so it's just zero. Assuming he stops accelerating at 100 mph, you would plug in your estimated a and get his displacement until he stops accelerating. Then you would take your own displacement of 90*t and subtract them for the difference. Then you could "rezero" it and set them equal to each other. So if the cop is something like 100 feet behind you when he hits 100, you would do 100*t=100 feet +90*t.

Or I guess if he'll continue accelerating until he catches you, setting .5at^2 = 90*t should also work.

Pretty sure that's how I would do it.

Post: #25

I always copied off the nerds next to me in that class