Analysis:

To find the maximum speed and distance acquired by the car, we need to analyze the given information and apply the equations of motion.

Given:
- Initial velocity (u) = 0 m/s (car starts from rest)
- First acceleration (a1) = 6 m/s^2
- Deceleration (a2) = -3 m/s^2 (negative because it is in the opposite direction to the initial acceleration)
- Total time of journey (t) = 10 seconds

Calculating maximum speed:
To find the maximum speed, we need to determine the time at which the car stops decelerating and starts moving with constant velocity.

Let's assume the time at which the car stops decelerating and starts moving with constant velocity is t1.

Since the car starts from rest and undergoes acceleration for t1 seconds, we can use the equation of motion:
v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Using this equation for the first part of the journey:
v1 = 0 + (6)t1
v1 = 6t1

After t1 seconds, the car starts decelerating with a constant negative acceleration of -3 m/s^2. The time taken for deceleration can be calculated as:
t2 = t - t1
t2 = 10 - t1

Using the equation of motion for deceleration:
v2 = v1 + a2t2
0 = 6t1 - 3(10 - t1)
0 = 6t1 - 30 + 3t1
0 = 9t1 - 30
9t1 = 30
t1 = 30/9
t1 ≈ 3.33 seconds

Substituting this value back into the equation for v1:
v1 = 6t1
v1 = 6(3.33)
v1 ≈ 19.98 m/s

Therefore, the maximum speed acquired by the car is approximately 19.98 m/s.

Calculating distance:
To determine the distance traveled by the car, we need to calculate the distances covered during acceleration and deceleration separately.

The distance covered during acceleration (S1) can be calculated using the equation:
S1 = ut + (1/2)at^2

Substituting the given values:
S1 = 0(3.33) + (1/2)(6)(3.33)^2
S1 = 0 + 9.99
S1 ≈ 9.99 m

The distance covered during deceleration (S2) can be calculated using the same equation, but with the negative acceleration:
S2 = v1t2 + (1/2)a2t2^2

Substituting the values:
S2 = 19.98(10 - 3.33) + (1/2)(-3)(10 - 3.33)^2
S2 = 139.86 - 65.02
S2 ≈ 74.84 m

The total distance traveled (S) is the sum of S1 and S2:
S = S1 + S2
S