Let's say you're driving in your car, approaching a red light on the Camp Hill Bypass. A black Porsche is stopped at the light in the right lane, but there's no-one in the left lane, so you pull into the left lane. You're traveling at 40 km/hr, and when you're 15 meters from the stop line the light turns green. You sail through the green light at a constant speed of 40 km/hr and pass the Porsche, which accelerated from rest at a constant rate of 3 m/s2 starting at the moment the light turned green.

(a) How far from the stop line do you pass the Porsche?
(b) When does the Porsche pass you?

(c) If a Boston police officer happens to get you and the Porsche on the radar gun at the in-stant the Porsche passes you, will either of you be pulled over for speeding? Assume the speed limit is 50 km/hr.

anyone good at physics? Help with this and my other question. Thankyou

To answer these questions, we need to calculate the distances traveled by both the car and the Porsche. Here's how we can approach each part:

(a) How far from the stop line do you pass the Porsche?

To determine the distance you travel until you pass the Porsche, we can first find the time it takes for the Porsche to reach your initial position (15 meters from the stop line) when the light turns green.

First, let's convert your initial speed from kilometers per hour (km/hr) to meters per second (m/s):
Speed = 40 km/hr = (40 * 1000) m / (60*60) s = 11.11 m/s

Now, let's calculate the time it takes for the Porsche to reach your initial position:
Using the equation:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2

Since the Porsche started from rest, its initial velocity is 0.

So, Distance = 0*Time + (1/2) * Acceleration * Time^2
Distance = (1/2) * 3 m/s^2 * Time^2
15 m = (1/2) * 3 m/s^2 * Time^2

Simplifying the equation, we have:
15 m = (3/2) m/s^2 * Time^2
Time^2 = (2/3) * (15 m) / (m/s^2)
Time = sqrt((2/3) * 15) s ≈ 3.87 s

Now that we know the time it takes for the Porsche to reach your initial position, we can find the distance you traveled until you pass the Porsche:
Distance = Speed * Time
Distance = 11.11 m/s * 3.87 s ≈ 42.97 m

Therefore, you pass the Porsche around 42.97 meters from the stop line.

(b) When does the Porsche pass you?

To determine when the Porsche passes you, we need to find the time it takes for both you and the Porsche to travel the same distance.

The distance traveled by the Porsche can be calculated using the equation:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Distance_Porsche = 0 * Time + (1/2) * 3 m/s^2 * Time^2
Distance_Porsche = (1/2) * 3 m/s^2 * Time^2

The distance traveled by you can be calculated using the equation:
Distance = Speed * Time
Distance_You = 11.11 m/s * Time

To find when the Porsche passes you, we set the two distances equal to each other and solve for Time:
(1/2) * 3 m/s^2 * Time^2 = 11.11 m/s * Time

Simplifying the equation, we have:
3/2 * Time^2 = 11.11 * Time
3/2 * Time^2 - 11.11 * Time = 0

Now, we can solve the quadratic equation to find the value(s) of Time when the Porsche passes you. Here, we will use the quadratic formula:
Time = (-b ± sqrt(b^2 - 4ac)) / 2a

For this equation, a = 3/2, b = -11.11, and c = 0.

Plugging these values into the quadratic formula, we get:
Time = (-(-11.11) ± sqrt((-11.11)^2 - 4*(3/2)*0)) / (2*(3/2))
Time = (11.11 ± sqrt(123.21 - 0)) / 3
Time = (11.11 ± sqrt(123.21)) / 3

Simplifying further, we have:
Time = (11.11 ± 11.1) / 3

There are two possible solutions:
Time = 22.21 / 3 ≈ 7.40 s
Time = 0.01 / 3 ≈ 0.003 s

Since the time cannot be negative, we discard the second solution.

Thus, the Porsche passes you at approximately 7.40 seconds after the light turns green.

To summarize:
(a) You pass the Porsche around 42.97 meters from the stop line.
(b) The Porsche passes you approximately 7.40 seconds after the light turns green.