# Bike Approaching Stopped Truck at Traffic Lights

• AltruistKnight
In summary, the cyclist was 7.5 m behind the truck when the traffic light turned green and the truck passed the cyclist at a distance of 12.5 m after 1 second.
AltruistKnight

## Homework Statement

A truck is stopped at a traffic light. The moment the light turns green, it begins to accelerate constantly at 3.1m/s^2. A cyclist approaching the truck from behind with a constant velocity of 10m/s was 7.5m behind the truck when the lights turned green.

1)How much time elapses between the light turning green and the bike passing the truck?
2)How long does it take for the truck to re-pass the bike?
3)How far has the truck traveled from the lights when it re-passes the bike?

## Homework Equations

This is a Kinematics question, so all the Kinematic Equations are applicable, which are as follows:
$$d=vit+1/2at^2$$
$$vf=vi+at$$
$$vf^2=vi^2+2ad$$

## The Attempt at a Solution

When the one passes the other, they would both have to be at the same position. I made their initial positions as "x" for the truck, and "x-7.5" for the bike. As the bike will gain on and pass the truck until they have the same speed, I know that the speed they will have when the bike first passes the truck will be less than or equal to the bike's initial speed. Unfortunately, I'm having difficulty seeing how the Kinematic Equations can get me started here. I get the feeling it'll involve some sort of quadratic, but I'm unsure of how to properly make the two aforementioned starting points of the truck and bike into a quadratic form, and from there how to derive additional values for my three Kinematic Equations.

The truck has accelerated motion so your d=Vit+1/2at² applies
What formula applies for the distance function of the bike in motion without acceleration?
Once you have your two d = formulas, taking the 7.5 m into account, you will solve by writing
truck distance = bike distance (maybe position would be a better term than distance)
then replace the two distances with your two formulas and solve the quadratic for t.

1 person
How would the 7.5 end up modifying the bike's equation? (I'm using d=Vit for it, I suspect it'd end up being Vit+7.5, since the bike's displacement would require it clear the 7.5m gap and as it reaches the final displacement where the truck is)

I wrote d = -7.5 + 10t for the bike so that at time zero it is 7.5 m behind from the truck's initial position.
It is way easier to write two formulas for the bikes position and the truck's position than to leap to the difference between them.

Ah, I see. -7.5 since the total distance the bike travels will be 7.5 more than that the truck traveled when they attain the same overall position. Thanks a lot, this problem was giving me a lot of grief.

The idea is to capture the motion of the bike in the formula. When you see d = -7.5 + 10t, think
t=0, d=-.7.5
t=1, d= 2.5 (past where the back of the truck was a second ago!)
t =2, d = 12.5
Now if you capture the truck's motion, too, you can work out where they are relative to each other. Formulas that tell everything about the motion as functions of time are tremendously powerful.
Another approach would be to graph them both on a d vs t graph. Of course these two equations are just the equations of the line for the bike and the parabola for the truck.

## What are the safety precautions for a bike approaching a stopped truck at traffic lights?

When approaching a stopped truck at traffic lights, it is important for cyclists to stay alert and follow these safety precautions:

• Always approach the truck from the left side and maintain a safe distance.
• Keep an eye out for any sudden movements or potential hazards, such as opening doors or debris on the road.
• Be aware of blind spots and avoid riding directly alongside the truck.
• Make sure to signal your intentions and communicate with the truck driver if necessary.
• Always follow traffic signals and laws, and yield to the truck if necessary.

## What should a cyclist do if they are stuck behind a stopped truck at traffic lights?

If a cyclist finds themselves stuck behind a stopped truck at traffic lights, they should follow these steps:

• Stay calm and maintain a safe distance from the truck.
• Look for an alternate route or a different lane to pass the truck.
• If passing is not possible, wait for the truck to start moving before proceeding.
• Communicate with the truck driver if necessary to ensure they are aware of your presence.
• Always prioritize safety and follow traffic laws.

## What are the potential dangers of a bike approaching a stopped truck at traffic lights?

The potential dangers of a bike approaching a stopped truck at traffic lights include:

• Being in the truck's blind spot, making it difficult for the driver to see the cyclist.
• The truck suddenly turning or changing lanes without warning.
• Opening doors or debris on the road that may cause the cyclist to lose control.
• Not following traffic signals and laws, increasing the risk of accidents.
• Not communicating with the truck driver, leading to misunderstandings and potential hazards.

## How can a cyclist ensure their safety when approaching a stopped truck at traffic lights?

To ensure their safety when approaching a stopped truck at traffic lights, cyclists should:

• Stay alert and aware of their surroundings at all times.
• Follow all traffic signals and laws.
• Communicate with the truck driver if necessary.
• Maintain a safe distance and avoid blind spots.
• Look for an alternate route or lane if passing the truck is not possible.

## What is the best way for a cyclist to communicate with a truck driver when approaching a stopped truck at traffic lights?

The best way for a cyclist to communicate with a truck driver when approaching a stopped truck at traffic lights is to:

• Make eye contact with the driver and use hand signals to indicate your intentions.
• Use a bell or horn to get the driver's attention, if necessary.
• Speak in a calm and respectful manner to avoid any misunderstandings.
• Be aware of any potential language barriers and try to communicate in a common language.
• Always prioritize safety and follow traffic laws.

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