You're approaching an intersection at 50 km/h (13.9 m/s ). You see the light turn yellow when you're 35 m from the intersection. Assume a reaction time of 0.6 s before braking begins and a braking acceleration of -3.0 m/s2.
A) will you be able to stop at before the intersection?
B) The yellow light stays on for 3.4 s before turning red. If you continue at 50 km/h without braking, will you make it through the 9.5-m-wide intersection before the light turns red?
d = 13.9 * .6 + (13.9/2)t
because average speed during deacceleration = half the original speed
time to stop during acceleration is t:
v = Vi + a t in general
so
0 = 13.9 - 3 t
t = 13.9/3
so in the end
d=13.9*.6 + (13.9/2)(13.9/3)
part b
will you go 35+9.5 meters in time?
what is 13.9 m/s * 3.4 seconds?
To answer these questions, we need to analyze the motion of the vehicle and calculate the stopping distance and time required.
A) To determine if you will be able to stop before the intersection, we need to calculate the stopping distance and compare it to the distance remaining.
1. Calculate the total distance covered during the reaction time:
Distance1 = Initial velocity * Reaction time
Distance1 = 13.9 m/s * 0.6 s
Distance1 = 8.34 m
2. Calculate the distance covered while braking:
Using the braking acceleration, we can use the kinematic equation to calculate the distance covered:
Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance
0^2 = (13.9 m/s)^2 + 2 * (-3.0 m/s^2) * distance
193.21 m^2/s^2 = 38.9 m^2/s^2 - 6.0 m/s^2 * distance
6.0 m/s^2 * distance = 155.31 m^2/s^2
distance = 155.31 m^2/s^2 / 6.0 m/s^2
distance ≈ 25.88 m
3. Calculate the total stopping distance:
Total distance = Distance1 + distance
Total distance = 8.34 m + 25.88 m
Total distance ≈ 34.22 m
Since the total stopping distance is less than the remaining distance of 35 m, you will be able to stop before the intersection.
B) To determine if you will make it through the intersection before the light turns red without braking, we need to compare the time it takes to cross the intersection with the time remaining until the light turns red.
1. Calculate the time required to cross the intersection:
Time = Distance / Velocity
Time = 9.5 m / 13.9 m/s
Time ≈ 0.6837 s
2. Calculate the time remaining until the light turns red:
Remaining time = Yellow light duration - Time taken to cross the intersection
Remaining time = 3.4 s - 0.6837 s
Remaining time ≈ 2.7163 s
Since the time remaining is greater than zero, you will be able to make it through the intersection before the light turns red without braking.