How far does the particle move in the x direction before turning around?

Question

a particle leaves the origin with an intial velocity of vector v = (2.4 m/s) x hat, and moves with a constant acceleration of vector a = (-1.9 m/s)x hat + (3.2m/s) y hat.

Answer 1

a particle leaves the origin with an initial velocity of vector v = (2.4 m/s) x hat, and moves with a constant acceleration of vector a = (-1.9 m/s^2)x hat + (3.2m/s^2) y hat.

Time = 2.4/1.9 = 1.263 sec.

At this time it is no longer moving in the x direction; the velocity in the x direction is zero.

Distance = average velocity times time

= (2.4 + 0)/2 * 1.263 =  1.5 m 2 significant figures.