Answer:
Let's solve this step by step:
a) Determine the distance over which the car accelerates
First, we need to find out how long the car travels before it starts to accelerate. The car travels for 1 second at a constant speed before the driver starts to accelerate. The distance covered in this time (d1) can be calculated using the formula:
d1 = v * t
where:
- v is the speed of the car = 40 km/h = 11.11 m/s (we convert km/h to m/s by dividing by 3.6)
- t is the time = 1 s
So, d1 = 11.11 m/s * 1 s = 11.11 m
The total distance the car needs to cover is the distance to the intersection plus the width of the intersection, which is 50 m + 15 m = 65 m.
Therefore, the distance over which the car accelerates (d2) is the total distance minus the distance covered before acceleration:
d2 = total distance - d1
= 65 m - 11.11 m
= 53.89 m
b) What is the speed of the car after it has completely passed the intersection?
The time left for acceleration is the total time for which the light is yellow minus the time taken by the driver to decide to accelerate, which is 5 s - 1 s = 4 s.
We can use the equation of motion to find out the final speed (v2) of the car:
v2^2 = v^2 + 2*a*d2
where:
- v is the initial speed of the car = 11.11 m/s
- a is the acceleration
- d2 is the distance over which acceleration occurs = 53.89 m
We know that a = (v2 - v) / t, where t is time for acceleration = 4 s.
Substituting a in our equation, we get:
v2^2 = v^2 + 2*((v2 - v) / t)*d2
Solving this equation for v2 gives us:
v2 = sqrt(v^2 + (2*d2*v/t))
Substituting values into this equation gives us:
v2 = sqrt((11.11 m/s)^2 + (2*53.89 m*11.11 m/s/4 s))
≈ sqrt(123.43 + 299.39)
≈ sqrt(422.82)
≈ 20.56 m/s
So, after completely passing through intersection, speed of car will be approximately **20.56 m/s** or **74 km/h** (converting m/s to km/h by multiplying by 3.6).
Step-by-step explanation: