Problem
Problem
Two particles are moving along x-axis. Particle-1 is 40 m behind particle-2. Particle-1 starts with velocity 12 m/s and acceleration 4 m/s2 both in positive x-direction. Particle-2 starts with velocity 4 m/s and acceleration 12 m/s2 also in positive x-direction. Find (a) the time when distance between them is minimum. (b) the minimum distance between them.Intuitive explanation
This is a relative motion problem where you need to track when (or if) the faster-accelerating particle catches up. The key insight is to write position equations for both particles and find when they're equal—but notice that particle-1 starts faster while particle-2 accelerates harder, so their relative speed changes over time. Set up and solve for ; you may find multiple solutions (or none), each telling you something about their motion.
Intuitive explanation
This is a relative motion problem where you need to track when (or if) the faster-accelerating particle catches up. The key insight is to write position equations for both particles and find when they're equal—but notice that particle-1 starts faster while particle-2 accelerates harder, so their relative speed changes over time. Set up and solve for ; you may find multiple solutions (or none), each telling you something about their motion.