Calculating Initial Velocity:
To find the time it takes for the car to come to rest, we first need to calculate its initial velocity. The car initially travels at a velocity of 72 km/h and decreases to 36 km/h.

Converting Velocity to m/s:
To work with the SI unit of velocity, we need to convert the given values from km/h to m/s.

- Initial velocity: 72 km/h = 20 m/s (1 km/h = 1000 m/3600 s)
- Final velocity: 36 km/h = 10 m/s

Calculating Acceleration:
Next, we can calculate the acceleration using the equation:

Acceleration (a) = (final velocity - initial velocity) / time

Since the car comes to rest, the final velocity is 0 m/s. Therefore, the equation becomes:

0 = (10 m/s - 20 m/s) / time

Simplifying the equation further:

-10 m/s = -20 m/s / time

Finding Time:
To find the time it takes for the car to come to rest, we can rearrange the equation:

time = -20 m/s / -10 m/s

The negative signs cancel out, leaving us with:

time = 2 seconds

Therefore, it will take the car 2 seconds to come to rest with the same acceleration.

Explanation:
When a car decreases its velocity, it undergoes deceleration or negative acceleration. The rate of change of velocity is given by the equation:

Acceleration (a) = (final velocity - initial velocity) / time

In this case, the final velocity is 0 m/s (as the car comes to rest), and the initial velocity is 20 m/s. We can rearrange the equation to solve for time:

time = (final velocity - initial velocity) / acceleration

Since the acceleration is given as -10 m/s, we substitute the values into the equation:

time = -20 m/s / -10 m/s

The negative signs cancel out, resulting in a positive time value of 2 seconds. Therefore, it will take the car 2 seconds to come to rest with the same acceleration.