Question

Two cars start off a race with velocities 2m`//`s and 4m`//`s travel in straight line with uniform acceleration `2m//s^(2) and 1m//s^(2)` respectively. What is the length of the path if they reach the final point at the same time ?

Answer 1

Let both particles reacl, at same position in same time t then from `s=ut+(1)/(2)at^(2)`
For `1^(st)` particle: `s=4(t)+(1)/(2)(1)t^(2)=4t+(t^(2))/(2)`. For `2^(nd)` particle : `s=2(t)+(1)/(2)(2)t^(2)=2t+t^(2)`
Equating above equation we get `4t+(t^(2))/(2)=2t+t^(2)rArrt=4sec`
Subsituting value of t in above equation `s=4(4)+(1)/(2)(1)(4)^(2)=16+8=24m`