Solving Police Car Overtaking Motorbike Problem

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In summary, the police car starts accelerating at 4ms-2 immediately after a motorbike traveling at 35ms-1 passes it. The police car keeps accelerating at this rate until it overtakes the motorbike. The police car travels 613m before overtaking the motorbike and the overtake occurs at 17.5 seconds. The distance traveled by both vehicles can be calculated using suvat equations and the expression for the distance traveled is a key factor in solving the problem.
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Ax3
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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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  • #2


Hint: write down the expression for the distance traveled by both vehicles.
 
  • #3


Thanks heaps radou! i figured it out
 
Last edited:

1. How can we reduce the number of accidents caused by police cars overtaking motorbikes?

One solution is to implement stricter protocols and training for police officers when it comes to overtaking motorbikes. This can include ensuring that the police car is equipped with proper sirens and lights, and that the officer is properly trained in using them. Additionally, implementing speed limits and designated passing zones can also help prevent accidents.

2. What factors contribute to accidents caused by police car overtaking motorbikes?

Some of the factors that can contribute to these accidents include: lack of proper training and protocols for police officers, excessive speed, failure to use sirens and lights, failure to signal when overtaking, and lack of designated passing zones.

3. Is there a technology that can assist in preventing these accidents?

Yes, there are technologies that can help prevent accidents caused by police cars overtaking motorbikes. These include proximity sensors that can alert the officer when they are too close to the motorbike, as well as automatic braking systems that can help avoid collisions.

4. How can we ensure the safety of both the police officer and the motorbike rider during an overtaking situation?

One way to ensure safety is by implementing proper training and protocols for police officers. This can include teaching them how to properly use sirens and lights, how to properly signal when overtaking, and how to determine safe passing zones. Additionally, implementing stricter consequences for officers who fail to follow these protocols can also help promote safety.

5. Is there a need for stricter laws or regulations regarding police car overtaking motorbikes?

There may be a need for stricter laws or regulations in some areas, depending on the frequency and severity of accidents caused by police car overtaking motorbikes. However, it is also important to consider the effectiveness of proper training and protocols in preventing these accidents before implementing stricter laws or regulations.

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