## A truck traveling at an average rate of 45 miles per hour leaves a rest stop. Fifteen minutes later s car traveling at an average rate of 60

Question

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## Answers ( No )

We write the kinematics equations

a

vf = a * t + vo

rf = (1/2) * a * t ^ 2 + vo * t + ro

We have then

For the truck:

a = 0vf = vo

rf = 45t

For the car:

a = 0vf = vo

rf = 60 * (t-15)

Matching rf:

45t = 60 * (t-15)

Clearing t:

45t = 60t-900

60t-45t = 900

15t = 900

t = 900/15 = 60h

Answer:it will take for the car to catch up with the truck 60hLet t = the time (hours) that the truck travels.

Because the car starts 15 minutes (or 0.25 hours) after the truck, the car travels for (t – 0.25) hours.

When the car catches up to the truck, both would have traveled the same distance.

The distance traveled by truck at 45 mi/h is

(45 mi/h)*(t h) = 45t mi.

The distance traveled by car at 60 mi/h is

(60 mi/h)*(t-0.25 h) = 60t – 15 mi.

Equate the two distances.

60t – 15 = 45t

60t – 45t = 15

15t = 15

t = 1

Answer: 1 hour