Solving the Speedster Puzzle: Calculating Time to Catch Up

In summary, the conversation is discussing a problem where a speeding motorist passes a stationary police officer and the officer begins pursuit with a constant acceleration. The question is how much time it will take for the officer to reach the speeder, assuming the speeder maintains a constant speed. The conversation mentions equations of motion and finding a solution using the equations.
  • #1
Sar06
4
0
I am stuck on this problem...
A speeding motorist traveling 120 km/h passes a stationary police officer. The officer immediately begins pursuit at a constant acceleration of 10.2 km/h/s (note the mixed units). How much time will it take for the police officer to reach the speeder, assuming that the speeder maintains a constant speed?
 
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  • #2
Do you have any equations of motion you are suppose to use?
 
  • #3
I know 3 equations of motion, but up until now I have only been looking for one variable or working with only one moving object... I'm not quite sure how to incorporate both moving objects into the equations I have. Could someone possibly lead me toward the process for finding the solution? Thanks.
 
  • #4
You know the distance will be the same so

d = vt
d = 1/2at^2

You can equate those

vt = 1/2at^2

Fix your units and solve.
 
  • #5
got it!

thank you so much. :smile:
 

FAQ: Solving the Speedster Puzzle: Calculating Time to Catch Up

How do you calculate the time it takes for a speedster to catch up to another object?

The time it takes for a speedster to catch up to another object can be calculated using the equation: T = D/(V2 - V1), where T is the time, D is the distance between the two objects, and V1 and V2 are the speeds of the two objects.

Can this equation be used for any type of speedster or object?

Yes, this equation can be used for any type of speedster or object as long as their speeds are constant and the distance between them is known.

What units should be used for the distance and speed in the equation?

The units used for the distance and speed should be consistent. For example, if the distance is measured in meters, the speed should also be measured in meters per second (m/s).

What if the speedster and object are moving in opposite directions?

If the speedster and object are moving in opposite directions, the speeds should be subtracted instead of added in the equation. This will result in a negative time, which indicates that the speedster will never catch up to the object.

Is there a more accurate equation for calculating the time to catch up for objects with varying speeds?

Yes, there is a more accurate equation that takes into account the changing speeds of the objects. It is known as the "time dilation" equation and is used in special relativity. However, for most practical situations, the basic equation provided in question 1 will suffice.

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