In a relay race, runner A is carrying the baton and has a speed of 5.6 ????/????. When runner A is 96 ???? behind runner B, runner A starts slowing down with 0.02 ????/???? 2 . At the same moment, runner B starts from rest and accelerates rightward with 0.06 ????/???? 2 . a) How long afterwards will A catch up with B to pass the baton to B? b) What are the speed of runners at the meeting point? c) What is the distance travelled by runner B at the meeting time?
Answer
Physics Behind Baton Passing in a Relay Race
Let’s analyze a real-world physics problem involving two runners during a relay race. One runner is decelerating while the other accelerates from rest. We’ll calculate:
- Time when Runner A catches up with Runner B
- Speeds of both runners at the meeting point
- Distance traveled by Runner B before receiving the baton
📘 Given:
- Runner A’s speed: vA = 5.6 m/s
- Runner A’s acceleration (deceleration): aA = -0.02 m/s²
- Initial gap between runners: 96 m
- Runner B starts from rest: vB = 0
- Runner B’s acceleration: aB = 0.06 m/s²
🧮 Step 1: Position Equations
Let’s define the origin where Runner A starts. Both runners are moving rightward.
xB(t) = 96 + 0.5 × 0.06t² = 96 + 0.03t²
🔄 Step 2: Set xA = xB to Find Time
Using the quadratic formula:
- t₁ = (-5.6 + 4)/-0.08 = -1.6 / -0.08 = 20 seconds ✅
- t₂ = (-5.6 – 4)/-0.08 = -9.6 / -0.08 = 120 seconds ❌ (too far)
✅ Runner A catches up to Runner B at t = 20 seconds
🏃♂️ Step 3: Find Speeds at Meeting Point
Runner A:
Runner B:
✅ Speeds at handoff: A = 5.2 m/s, B = 1.2 m/s
📏 Step 4: Distance Runner B Covers
✅ Runner B travels 12 meters before receiving the baton
🧠 Summary
- ⏱️ Time to catch up: 20 seconds
- 🏃 Speed of Runner A: 5.2 m/s
- 🏃♂️ Speed of Runner B: 1.2 m/s
- 📍 Distance B runs: 12 meters
🎯 Concepts Used:
- ✔️ Position-time equations for uniformly accelerated motion
- ✔️ Relative motion between two moving objects
- ✔️ Quadratic formula for solving time
💬 Conclusion
This example shows how simple kinematic equations can be applied to real-world scenarios like sports. Relay races involve more than just speed — understanding acceleration and timing is key to a successful handoff!