To solve this problem, we need to analyze the motion of the car and the ball separately.$\\$1. Motion of the Car:$\\$• The car starts from rest and accelerates at $5$ m/s$^2. \\$• The velocity of the car at $t = 4$ s is given by the equation:$\\ v_{car} = u + at \\ v_{car} = 0 + 5 \times 4 \\ v_{car} = 20$ m/s$\\$2. Motion of the Ball:$\\$• At $t = 4$ s, the ball is dropped from the car.$\\$• The initial velocity of the ball is the same as the velocity of the car at that moment,$\\ v_{ball, initial} = 20$ m/s$. \\$• The ball is subject to gravity only after being dropped, so its acceleration is $g = 10$ m/s$^2$ downward.$\\$3. Velocity of the Ball at $t = 6$ s:$\\$• The time elapsed since the ball was dropped is $6 - 4 = 2$ s.$\\$• The velocity of the ball at $t = 6$ s is given by:$\\ v_{ball} = v_{ball, initial} + g \cdot t_{elapsed} \\ v_{ball} = 20 + 10 \times 2 \\ v_{ball} = 20 + 20 \\ v_{ball} = 40$ m/s$\\$4. Acceleration of the Ball at $t = 6$ s:$\\$• Once the ball is dropped, it is only under the influence of gravity.$\\$• Therefore, the acceleration of the ball is $10$ m/s$^2$ downward.$\\$Thus, the velocity and acceleration of the ball at $t = 6$ s are $40$ m/s and $10$ m/s$^2$ respectively.$\\$This corresponds to Option 4.