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 respectivelyfor 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 pointx = 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).

Two particles 1 and 2 start simultaneously from origin and move along

1.	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 respectivelyfor 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 pointx = 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» 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))`