Crossing and catching problems

Catch problems: write both positions, set them equal, solve for time.

Crossing and catching problems0 min · Free lecture

In this lesson

  • Catch problems: write both positions, set them equal, solve for time.

A police car chasing a speeding car — the catch happens when positions coincide, not when speeds match.

For two bodies, write x₁(t) and x₂(t) in one frame with the same origin. Catch/meet: x₁ = x₂. Solve for t, then back-substitute.

If one starts later or from a different point, encode that in its initial position. If the chaser accelerates, its displacement is ½at².

x1(t)=x2(t)x_1(t) = x_2(t)

The catch condition

Worked example

The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.

  1. Area under the a–t graph = change in velocity.
  2. Area = 2 m/s² × 4 s = 8 m/s (the last 2 s add nothing).

Answer: 8

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Crossing and catching problems — FemtoLearn.
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Catch problems: write both positions, set them equal, solve for time.
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Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 2/5

    The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.

  2. Q2 · MCQ · difficulty 2/5

    A particle moves with constant velocity. Which a–t graph describes it?

    • A horizontal line at a = 0
    • A horizontal line at a = 2 m/s²
    • A straight line through the origin
    • A parabola
  3. Q3 · Numerical · difficulty 2/5

    A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance