a particle starts from rest at A and moves with uniform acceleration a m/s^2 in a straight line after - Physics - Motion In A Plane

Question

a particle starts from rest at A and moves with uniform
acceleration a m/s^2 in a straight line after 1/a seconds a second
particle starts from A and moves wuth uniform velocity u in the
same line and direction if u>2m/s then during the entire motion
the second particle remains ahead of the first particle for a
duration

Pratyay Ghosh · Accepted Answer

Lets say that they meet after t sec of particle 1's start
The distance travelled by particle 1=distance travelled by particle
2
12at2=u(t-1a)⇒at2=2ut-2ua⇒at2-2ut+2ua=0⇒t=u±u2-2ua
Now t has two values For The time in between these two solutions,
particle 2 remains ahead of particle 1 The time duration is
Δt=u+u2-2ua-u-u2-2ua=2u2-2ua