Solving Police Car Overtaking Motorbike Problem

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The discussion revolves around a physics problem involving a police car accelerating to overtake a speeding motorbike. The motorbike travels at a constant speed of 35 m/s, while the police car accelerates at 4 m/s². The solution requires calculating the distance the police car travels before overtaking the motorbike, which is 613 meters, and the time it takes to do so, which is 17.5 seconds. The initial attempts to solve the problem using the suvat equations were challenging, particularly in understanding the relationship between the velocities of both vehicles. Ultimately, the participant found clarity in the approach needed to solve the problem.
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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
 
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