Understanding the Problem:

We are given that a car starts from rest and accelerates at a constant rate of 2 m/s² for some time. After that, it decelerates at a constant rate of 4 m/s² until it comes to rest. We need to determine the maximum speed attained by the car if it remains in motion for 3 seconds.

Solution:

To solve the problem, we can break it down into two parts - the acceleration phase and the deceleration phase.

Acceleration Phase:
During the acceleration phase, the car starts from rest and accelerates at a constant rate of 2 m/s². We need to find the speed attained by the car at the end of this phase.

Using the equation of motion:
v = u + at

Where:
v = final velocity
u = initial velocity (0 in this case as the car starts from rest)
a = acceleration (2 m/s²)
t = time (unknown)

Substituting the given values into the equation, we have:
v = 0 + 2t
v = 2t

Deceleration Phase:
During the deceleration phase, the car decelerates at a constant rate of 4 m/s² until it comes to rest. We need to find the time taken for the car to come to rest.

Using the equation of motion:
v = u + at

Where:
v = final velocity (0 as the car comes to rest)
u = initial velocity (speed attained at the end of the acceleration phase, which is 2t)
a = acceleration (-4 m/s² as the car is decelerating)
t = time (unknown)

Substituting the values into the equation, we have:
0 = 2t - 4t
0 = -2t
t = 0

From the equation, we can see that the car comes to rest at t = 0, which means the deceleration phase lasts for 0 seconds.

Maximum Speed:
To find the maximum speed attained by the car, we need to determine the speed at the end of the acceleration phase. From the equation v = 2t, we can substitute t = 3 seconds (as given in the problem).

v = 2 * 3
v = 6 m/s

Therefore, the maximum speed attained by the car is 6 m/s.

Summary:
- The car starts from rest and accelerates at a constant rate of 2 m/s².
- The car decelerates at a constant rate of 4 m/s² until it comes to rest.
- The deceleration phase lasts for 0 seconds.
- The maximum speed attained by the car is 6 m/s.

6 ms-1