Question

A highway patrolman traveling at the speed limit is passed by a car going 20 mph faster than the speed limit. After one minute, the patrolman speeds up to 115 mph. How long after speeding up until the patrolman catches up with the speeding car. The speed limit is 55 mph.
(b) Same question, but this time the patrolman speeds up to a speed of v mph

Answer 1

The cop is going 55 mph while the other car is going 55+20 = 75 mph.

How many miles does the other car drive in one minute?

Answer 2

1.25

Answer 3

correct

Answer 4

A highway patrolman traveling at the speed limit is passed by a car going 20 mph faster than the speed limit. After one minute, the patrolman speeds up to 115 mph. How long after speeding up until the patrolman catches up with the speeding car. The speed limit is 55 mph.

civilian car
v=20
x = 20*t

police car
x = 1/2 * a t^2 +

Answer 5

right so a is .5 but I cant solve b)

Answer 6

The cop will travel approximately D = r*t = 55*(1/60) = 0.91667 miles in one minute.


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let t = time elapsed since the other car passed the cop


from t = 0 to t = 1, the cop travels approximately 0.91667 miles
at t = 1, the cop now goes 115 mph
So the cop goes an additional 115(t-1) miles where t > 1.

The equation for the cop is y = 115(t-1)+0.91667 where t > 1

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from t = 0 to t = 1, the other car travels 1.25 miles
then from t = 1 to some time in the future, call it t, the car will travel an additional 75t miles


The equation for the other car is y = 75t + 1.25

Answer 7

to find out when they meet, you set the two distances equal to each other

you would get

115(t-1)+0.91667 = 75t + 1.25

solve for t

Answer 8

then again, the change will be gradual

Answer 9

I got 2.88333325 ???

Answer 10

Assuming he starts at 55 mph at t = 0, then accelerates to 115 mph when t = 1 rolls around, the cop would travel


d = (1/2)*(vf + vi)*t

d = (1/2)*(115+55)*(1/60)

d = 1.41667


So he travels roughly 1.41667 miles from t = 0 to t = 1. Then you'd add on 115(t-1)

So it would slightly alter the answer. This is assuming you know the formula d = (1/2)*(vf + vi)*t

Answer 11

I wasn't thinking of the gradual acceleration

Answer 12

I'm using this btw

http://www.studyphysics.ca/newnotes/20/unit01_kinematicsdynamics/chp04_acceleration/images/formulas.GIF

the last equation at the very bottom

Answer 13

So I think you need to solve this instead

115(t-1)+1.41667 = 75t + 1.25

but I'd get a second opinion since I'm not 100% sure

Answer 14

nope :(

Answer 15

neither equation works?

Answer 16

let me think of where I might be going wrong

Answer 17

Let X = point where they meet

Answer 18

once you make a table, the equations become obvious