Two particles 1 and 2 start simultaneously from origin and move along the positive X direction. Initial velocity of both particles is zero. The acceleration of the two particles depends on their displacement (x) as shown in fig.

(a) Particles 1 and 2 take `t_(1)` and `t_(2)` time respectively for their displacement to become `x_(0)`. Find `(t_(2))/(t_(1))`.
(b) Which particle will cover `2x_(0)` distance in least time? Which particle will cross the point `x = 2x_(0)` with greater speed?
(c) The two particles have same speed at a certain time after the start. Calculate this common speed in terms of `a_(0)` and `x_(0)`.

Answer

(a) `sqrt(2)` (b) particle 1 will cover `2x_(0)` in lesser time. Both will cross `2x_(0)` with same speed. (c) `v = (2 +sqrt(2)) sqrt(a_(0)x_(0))`