Solving the Speedster Puzzle: Calculating Time to Catch Up

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To solve the problem of a speeding motorist and a pursuing police officer, the key is to use the equations of motion effectively. The motorist travels at a constant speed of 120 km/h, while the officer accelerates at 10.2 km/h/s. By equating the distance formulas for both the motorist and the officer—d = vt for the motorist and d = 1/2at^2 for the officer—one can find the time it takes for the officer to catch up. It's important to ensure consistent units throughout the calculations. The solution involves fixing the units and solving the resulting equation.
Sar06
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I am stuck on this problem...
A speeding motorist traveling 120 km/h passes a stationary police officer. The officer immediately begins pursuit at a constant acceleration of 10.2 km/h/s (note the mixed units). How much time will it take for the police officer to reach the speeder, assuming that the speeder maintains a constant speed?
 
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Do you have any equations of motion you are suppose to use?
 
I know 3 equations of motion, but up until now I have only been looking for one variable or working with only one moving object... I'm not quite sure how to incorporate both moving objects into the equations I have. Could someone possibly lead me toward the process for finding the solution? Thanks.
 
You know the distance will be the same so

d = vt
d = 1/2at^2

You can equate those

vt = 1/2at^2

Fix your units and solve.
 
got it!

thank you so much. :smile:
 
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