Solving Police Car Overtaking Motorbike Problem

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SUMMARY

The problem involves a police car accelerating from rest at 4 m/s² to overtake a motorbike traveling at a constant speed of 35 m/s. The police car travels a total distance of 613 meters before overtaking the motorbike, which occurs at 17.5 seconds. The solution requires the application of kinematic equations, specifically the SUVAT equations, to calculate the distance and time accurately. The key to solving the problem lies in setting up the equations for distance traveled by both vehicles and equating them to find the point of overtaking.

PREREQUISITES
  • Understanding of SUVAT equations in kinematics
  • Basic knowledge of acceleration and velocity concepts
  • Ability to set up and solve algebraic equations
  • Familiarity with motion graphs and their interpretations
NEXT STEPS
  • Study the derivation and application of SUVAT equations in various motion problems
  • Learn how to graphically represent motion using velocity-time and distance-time graphs
  • Explore real-world applications of kinematics in vehicle motion analysis
  • Practice solving similar problems involving relative motion and acceleration
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This discussion is beneficial for physics students, educators, and anyone interested in understanding kinematic problems involving acceleration and relative motion. It is particularly useful for those preparing for exams or tackling homework in mechanics.

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Homework Statement


"A speeding motorbike travels past a stationary police car at a speed of 35ms-1. The police car starts accelerating immediately at 4ms-2, and keeps accelerating at this rate until it has passed the bike.

- How far has does the police car travel before it overtakes the motorbike? (Ans=613m)
- At what time does the police car overtake the motorbike? (Ans=17.5s)

The Attempt at a Solution



I have tried using a suvat equation, namely v=u+at to calculate the time taken for the police car to catch up to the motorbike (where i use v=35), however obviously the police car will never catch up to the bike if it only matches its velocity.. I'm really unsure of what to do next because trial and error using suvat equations has not provided me with much assistance.

Thanks in advance for any help! (Im just after some clarification as the steps i would need to take/variables i would need to identify in order to answer a question similar to this)
 
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Hint: write down the expression for the distance traveled by both vehicles.
 


Thanks heaps radou! i figured it out
 
Last edited:

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