Background knowledge:

For cars traveling along dufferin,the speed is 60km/h. The distance to cross the intersection is 34m. Assume the length of a typical car is 4.5m. For safety reasons, the Ministry of Transportation recommends that vehicles stop with an acceleration no higher than 3.0m/s2

Question
How much distance(in m) will it take a car to stop when a light turns yellow if it is traveling at the speed limit of 60km/h? Drivers do not react right away when they see the light change; human reaction time is between 0.50s and 1.0s. in your calculation, assume the driver does not react for 1.0s. in other words, the car continues to travel at the speed for 1.0s after the light has turned. Then the driver brakes to a stop at an acceleration of 3.0m/s2

thank you

r = 60km/h = 60,000m/3600s. = 16.67 m/s.

d = d1 + d2

d1 = r*t = 16.67m/s * 1s = 16.7 m.

d2 = (V^2-Vo^2)/2a
d2 = (0-(16.7)^2/-6 = 46.3 m.

d = 16.7 + 46.3 = 63.0 m.

To find the distance it will take for a car to stop when the light turns yellow, we need to consider two components: the distance covered during the driver's reaction time and the distance covered while braking.

First, let's calculate the distance covered during the driver's reaction time. We know the speed of the car is 60 km/h, which is equivalent to 16.67 m/s. The reaction time is given as 1.0 second. Therefore, the distance covered during this time is:

Distance covered during reaction time = Speed × Reaction time
= 16.67 m/s × 1.0 s
= 16.67 m

Next, let's calculate the distance covered while braking. We have the acceleration of the car, which is given as 3.0 m/s². To find the time it will take for the car to come to a stop, we can use the equation of motion:

v² = u² + 2as

where:
v = final velocity (0 m/s, since the car comes to a stop)
u = initial velocity (16.67 m/s)
a = acceleration (-3.0 m/s²)
s = distance

Rearranging the equation, we have:

0 = (16.67 m/s)² + 2(-3.0 m/s²)s

Simplifying further:

0 = 277.78 + (-6.0)s
6.0s = 277.78
s = 277.78 / 6.0
s ≈ 46.30 m

Therefore, the distance covered while braking is approximately 46.30 meters.

Now, we can calculate the total distance covered to stop by adding the distance covered during the reaction time and the distance covered while braking:

Total distance to stop = Distance covered during reaction time + Distance covered while braking
= 16.67 m + 46.30 m
= 62.97 m

Hence, it will take approximately 62.97 meters for the car to stop when the light turns yellow.