How Long Does It Take for a Car to Pass a Truck After Reaching the Speed Limit?

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A car accelerates from 20 m/s to 25 m/s while behind a truck moving at 18 m/s, starting 50 m behind it. The car's acceleration is 1.8 m/s², and it takes approximately 2.78 seconds to reach the speed limit. During this time, the car travels 62.5 m, while the truck covers 50 m, leaving a gap of 37.5 m between them. To determine how long it takes for the car to overtake the truck, the relative distance and speeds are used, leading to a calculated time of about 5.2 seconds from when the car reaches the speed limit until it passes the truck. Understanding the relationship between their speeds and distances is crucial for solving the problem.
  • #31
37.5 m? if the car starts at the origin, then its final position would be 62.5m and the truck starts at 50, its final position would be 100 m
 
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  • #32
Perfect. Now? :)
 
  • #33
im not sure which equation to use.
 
  • #34
Ok you know the distance between the car and truck, and you know their speeds and you need to find the time.

In terms of relative velocity, its just distance = relative velocity*time

But in case you're not familiar with relative velocity, look at it like this. Assume the car takes time T to overtake the truck. It moves a distance 25*T during this. The truck moves a distance 18*T in the meantime. Now, The car should move 37.5 m more than the truck to overtake it.
 

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