Driving/Kinematics Question

[MJC8719]

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 5.5 mi/h, the time to go one mile decreases by 12 s. What was your original speed?

hey yall, so I am sure that this is probably an easy question but I am getting stuck,

heres what i have so far

So my original speed is v = 1/t miles/s

Second hint: New speed = v + 5.5 = (1/t + 5.5)

Time to go 1 mile decreesed by 12 sec means it took (t-12) sec to travel one mile this time.

So new speed can also be written as 1/(t-12)
1/t + 5.5 = 1 /(t-12)

so i then solved for t,

this gave me t-12.179 seconds. i then thought that my original speed would be 1/t miles/s

so i divided 1/12.179 = .082108 miles per second.

i think thought to multiply this by 60 to convert to minutes then again by 60 to convert to hours. this gave me 295.59077 as my final answer which isn't correct. according to the homework problem, it is between 10 to 100% off the correct answer.

also, i will add this nother question to this thread...

While riding on an elevator descending with a constant speed of 2.8 m/s, you accidentally drop a book from under your arm.

How long does it take for the book to reach the elevator floor, 1.1 m below your arm?

What is the book's speed relative to you when it hits the elevator floor?

I got this first part of this fine..the answer was .4738 seconds but cannot get the second.

I am assuming that the velocity of the book would be simply found by dividing distance by time so...1.1/.4738 = 2.32165 m/s or...i also was given the formula

final velocity = square root of (initial velocity - 2 x acceleration x displacement)

this equation gave me a final velocity of 4.6432 m/s

i am unsure which is the correct one and why...also then how to i compare this veolocity relative to me...add or subtract or multiply...? i do not understand that part.

thanks for any and all help

 

[cepheid]

You overlooked the fact that the increase in speed, 5.5, was given in miles per HOUR not, miles per second. Convert the 5.5, and redo the calculation. Alternatively, convert the 12 s to hours from the start.

 

[cepheid]

For the second question, you can't just divide the distance the book fell by the time it took to fall, because the book isn't traveling at a constant velocity. It's accelerating. Doing that would only give you its average velocity over that time interval. That's why the other formula has to be used.