Two race cars are at the track during a qualifying session. The combined mass of car A and its driver is 840 kg. The combined mass of car B and its driver is 810 kg. Car A is moving to the right at 3.0 m/s and is 16 m behind car B, as shown in the diagram below. The driver loses control and collides with car B, which is at rest.

$1.$ Car A accelerates at $1\mathrm{.}5$ m$/$s$2$ to a speed of $6\mathrm{.}0$ m$/$s and then continues at constant velocity until it strikes car B$.$ Calculate the total time for car A to travel the $16$ m$.(4$ points$)$$\mathrm{}$

$2.$ i$)$ After the collision, car B moves to the right at a speed of $4\mathrm{.}6$ m$/$s$.$Calculate the speed of car A after the collision. $(3$ points$\mathrm{) }$

ii$)$ Indicate the direction of motion of car A after the collision. Justify your response. $(3$ points$)$$\mathrm{}$

$3.$ Is this an elastic collision? Justify your response. $(5$ points$)$

3.0 m/s A 16 m B