Calculate Initial Speed Driving on a Crowded Freeway

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Homework Help Overview

The problem involves calculating the original speed of a vehicle driving on a crowded freeway, given the time taken to travel between mile markers and the effect of an increase in speed on travel time. The subject area pertains to kinematics and speed-time relationships.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between speed, distance, and time, with attempts to formulate equations based on the given conditions. Some express uncertainty about the correct approach, while others suggest converting units for consistency.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have offered guidance on unit conversion and basic formulas, while others are still grappling with how to set up the equations needed to find the original speed.

Contextual Notes

There is a noted difficulty in aligning the units of speed (miles per hour) with time (seconds), which some participants mention as a barrier to finding a solution. Additionally, the original poster expresses frustration over not having a clear formula to apply.

Robb380
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Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 4.5 mi/h, the time to go one mile decreases by 9 s. What was your original speed?

I've been working on this for 2 hours, I can't seem to get the formula right.
 
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Welcome to PF!

Hi Robb380! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
I've decided that the v=d/t is not the way to go and that (vi) initial velocity is vi- 4.5mph=vf or final velocity (vf) = vi + 4.5 mph. and the time is t-9. going 1 mile gives me
initial distance= 0
final distance= 1
initial velocity(vi)= vf-4.5 mph
final velocity(vf)= vi+4.5
time for (vi) mph= t
time for (vf) mph=t-9
What i can't seem to do is find an equation that can help me find the initial velocity. I've tried different ones but they don't see to fit well, I am thinking i can solve for t and from there find (vi) but I am not sure how
 
First of all, I suggest you convert your speeds to common units. You have speed in miles per hour and time in seconds. A better approach would be to convert the change in speed, 4.5 mph, to the equivalent speed in feet per second.

You know that at your original speed, it took ti seconds to travel 1 mile, or 5280 feet. After increasing speed by 4.5 mph, it took 9 fewer seconds to travel 1 mile. Think you can work out the original speed now?
 
Not really because I don't have a formula to use to solve for anything, i tried a binomial equation but that came out wrong, I retraced to see if I wasn't converting the units but I was, I tried putting everything into miles per second but I keep getting stuck when trying to solve for t so that I can solve for (vi). What I need is to figure out is how to get either (ti), (vi), or i might need both
 
It's a simple problem to set up. The only formula you need is v = d / t and a little algebra.
 
Hi Robb380! :smile:
Robb380 said:
Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next.

So the initial speed is obviously 1/t mph, isn't it? :wink:

Carry on from there …

what do you get? :smile:
 
Last edited:
Robb380 said:
Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next.

tiny-tim said:
Hi Robb380! :smile:


So the initial speed is obviously t mph, isn't it? :wink:
Assuming that t is measured in hours.
 

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