Motion in a Straight Line

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is .

Answer

3

Solution

xP-xQ=(uP-uQ)t+ (a0-a')t22+ kt36 — a cubic in t; crossing ⇒ xP-xQ=0

[figure]

t=0 is one root; the other factor is a quadratic with at most 2 positive roots

∴ maximum crossings =1+2=3

Answer: 3