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Chase and meeting problems
Intermediate
Equate positions at the meeting time to solve for it.
Write the position of each body as a function of time and set the positions equal to find the meeting time. Be careful with different start times and directions.
A at 10 m/s starts 100 m behind B at 5 m/s: 10t = 100 + 5t → t = 20 s.
Check that the meeting time is positive and within the motion range.
In more detail
Chase problems find when and where two moving objects meet, by setting their positions equal as functions of time. Relative velocity helps decide whether they close the gap.
Real-world uses
- Police chases and sports interception problems use this type of analysis.
- Traffic planners estimate when a faster vehicle will catch a slower one.
- A runner chasing a bus or two cyclists meeting on a road both use the idea of equal positions at the same time to solve the problem.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How do I solve a chase problem?
Write both position functions, set them equal and solve for the time.
What if they never meet?
If the equation has no positive solution, the objects never meet in the given motion.
What is the first step in a chase problem?
Write each object's position as a function of time, starting from the same origin, then set the two positions equal.
Related topics in Kinematics
Galilean transformation · Frames: inertial vs non-inertial · Coriolis and fictitious motion · Average vs instantaneous acceleration