Time & Velocity Homework: Police Car Overtake Speeder

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Homework Help Overview

The problem involves a scenario where a speeder passes a stationary police car, which then accelerates to catch up. The speeder travels at a constant speed, while the police car accelerates uniformly. Participants are tasked with determining the time it takes for the police car to overtake the speeder.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations of motion for both the police car and the speeder, questioning how to set their displacements equal to find the time of overtaking. Some participants express confusion over their calculations and seek clarification on the correct approach.

Discussion Status

Some participants have attempted calculations and shared their results, while others are exploring different methods to arrive at the solution. There is an ongoing dialogue about the correct equations to use and the assumptions involved in the problem.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a focus on ensuring that both vehicles are at the same position at the same time for the overtaking to occur.

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Homework Statement


A speeder passes a parked police car at a constant speed of 27.6 m/s. At the instant, the police car starts from rest with a uniform acceleration of 2.27 m/s^2. How much t passes before the speeder is overtaken by the police car.


I tried solving for t using t=Vf-Vi /a and i get 12.15sec, which is wrong what am i doing wrong?
 
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bigzee20 said:

Homework Statement


A speeder passes a parked police car at a constant speed of 27.6 m/s. At the instant, the police car starts from rest with a uniform acceleration of 2.27 m/s^2. How much t passes before the speeder is overtaken by the police car.

I tried solving for t using t=Vf-Vi /a and i get 12.15sec, which is wrong what am i doing wrong?

Observe that to catch him they must both be at the same X at the same Time.

What is the equation for the PoPo's displacement with respect to time?
And for the reckless miscreant?

When they are equal, it's book'em Danno.
 
OMMMMG I love u I GOT IT!
x=1/2a(t)^2 + Vi(t)

Cops= 1/2(2.27)(12.15)+0(12.15) = 13.79025
Speeder= 1/2(0)12.15+27.6(12.15) = 335.34
335.34/13.79025 = 24.32s
 
Last edited:
bigzee20 said:
OMMMMG I love u I GOT IT!
x=1/2a(t)^2 + Vi(t)

Cops= 1/2(2.27)(12.15)+0(12.15) = 13.179025
Speeder= 1/2(0)12.15+27.6(12.15) = 335.34
335.34/13.179025 = 24.32s

??

I was thinking of something considerably more direct.

1/2*a*t2 = V * t

t = 2*V/a = 2*27.6/2.27 = 24.32 s
 

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