When you see a traffic light turn red, you apply the brakes until you come to a stop. Suppose your initial speed was 12.9 m/s, and you come to rest in 35.0 m. How much time does this take? Assume constant deceleration.

What is your question about this problem? I will be happy to critique your thinking. We are not in the habit of doing homework or tests for students.

how to do it

To find out how much time it takes for a car to come to a stop, given its initial speed, distance traveled, and assuming constant deceleration, we can use the kinematic equation:

v² = u² + 2as

Where:
- v is the final velocity (which is zero since the car comes to a stop),
- u is the initial velocity,
- a is the acceleration,
- s is the distance traveled.

In the given problem, the initial velocity, u, is 12.9 m/s and the distance traveled, s, is 35.0 m.

Rearranging the equation, we get:

a = (v² - u²) / (2s)

Since the final velocity, v, is zero, we can simplify the equation to:

a = - u² / (2s)

Substituting the known values:

a = - (12.9 m/s)² / (2 * 35.0 m)

Calculating this expression gives us:

a ≈ - 7.37 m/s²

Now, we can use another kinematic equation to find the time, t, it takes for the car to come to a stop:

v = u + at

Since v is zero, the equation becomes:

0 = 12.9 m/s + (-7.37 m/s²) * t

Rearranging, we have:

7.37 m/s² * t = 12.9 m/s

Now, divide both sides by 7.37 m/s² to isolate t:

t = 12.9 m/s / 7.37 m/s²

Calculating this expression gives us:

t ≈ 1.75 seconds

Therefore, it would take approximately 1.75 seconds for the car to come to a stop.