An automobile is traveling 65mph. Its brakes decelerates at 6.0mps. How long will it takes to stop the car?

To find out how long it will take to stop the car, we need to use the formula of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the car comes to a stop)
u = initial velocity (65 mph, which we need to convert to meters per second)
a = deceleration (-6.0 m/s^2, as it is decelerating)
s = displacement (unknown, as it is the time we want to find)

First, we need to convert the initial velocity from mph to m/s. To convert mph to m/s, we can use the following conversion factor:

1 mph = 0.44704 m/s

So, the initial velocity, u, in m/s would be:

u = 65 mph * 0.44704 m/s = 29.0576 m/s (approximately)

Now, let's plug the values into the formula:

(0 m/s)^2 = (29.0576 m/s)^2 + 2 * (-6.0 m/s^2) * s

Simplifying the equation:

0 = 843.2681 m^2/s^2 - 12.0 m/s^2 * s

Rearranging the equation to solve for s:

12.0 m/s^2 * s = 843.2681 m^2/s^2

s = 843.2681 m^2/s^2 / 12.0 m/s^2

s ≈ 70.2723 m

Finally, we can determine the time it takes to stop the car by using the formula:

t = (v - u) / a

t = (0 m/s - 29.0576 m/s) / -6.0 m/s^2

t ≈ 4.84293 s

Therefore, it will take approximately 4.84293 seconds for the car to come to a complete stop.