Particles A and B travel along a straight road in the positive x direction. Their velocities change abruptly at t=4 seconds but remain constant between these times. Position is measured in meters from x=0, where both particles are located at t=0.
• For 0≤t≤4: vA=6 m/s and vB=3 m/s, with xA(0)=0 and xB(0)=10.
• For t≥4: vA=2 m/s and vB=5 m/s.
Assume each particle’s velocity changes instantaneously at t=4 but its position remains continuous.
(1) Determine the positions xA(4) and xB(4). State which particle is ahead at t=4 and by how many meters.
(2) Explain whether the two particles can meet at any time with 0<t<4. Support your conclusion with an appropriate calculation or inequality.
(3) For t≥4, decide whether the particles meet. If they do, find the time t and position x of the meeting; if they do not, provide a clear justification.
(4) Describe qualitatively how the change in each particle’s velocity at t=4 affects the long-term separation between the particles. Relate your discussion to the signs and magnitudes of their relative velocity before and after t=4.