# Finding the distance at which Car 1 overtakes Car 2

In summary: So the correct equation should be 86km/hr (t) + 30km = 106km/h (t). Solving for t gives t = 30 km / (106 km/hr - 86 km/hr) = 60 seconds. Therefore, car A will travel 86 km/hr * 60 s = 5160 km before being overtaken by car B.
Problem 1:
Two cars are traveling along a straight road. Car A maintains a constant speed of 86 km/h; car B maintains a constant speed of 106 km/h. At t = 0, car B is 30 km behind car A. How far will car A travel from t = 0 before it is overtaken by car B?

Problem 2:
At t = 0, a stone is dropped from a cliff above a lake; 1.5 seconds later another stone is thrown downward from the same point with an initial speed of 31 m/s. Both stones hit the water at the same instant. Find the height of the cliff.

These are two problems that came up on the homework, and I still am unable to solve them. I am able to get all the problems with one object involved, I just don't seem to comprehend how to set these up and solve them. Any help is appreciated.

Equations in this chapter:
v = v0+at
$\Delta$x=v0t+1/2at2
vav=1/2(v0+v)

I have tried graphing the problems to understand them, but I think I am lacking the fundamental understanding of what each should look like. I have reread the chapter and I am still in the same boat. Text book: Physics for Scientists and Engineers 5th ed.

Welcome to Physics Forums.

HINT: When the two cars/stones overtake/hit the water, their relative displacements will be zero. In order words you are looking for the distance when their two positions are the same.

Thanks for the hint and the welcome!

For the first problem, I am assuming the acceleration is 0. Therefore, I can use the 2nd formula as delta x = (v0)t

I believe delta x of car A would be 86km/hr (t) and delta x of car B would be 106 km/hr (t). To find where they have the same displacement, I am guessing I set it up as 86km/hr (t) = 106km/h (t) + 30km
Solve for t, t = 30 km / (86km/hr - 106 km/hr).

Seem to be the right track?

Thanks for the hint and the welcome!

For the first problem, I am assuming the acceleration is 0. Therefore, I can use the 2nd formula as delta x = (v0)t

I believe delta x of car A would be 86km/hr (t) and delta x of car B would be 106 km/hr (t). To find where they have the same displacement, I am guessing I set it up as 86km/hr (t) = 106km/h (t) + 30km
Solve for t, t = 30 km / (86km/hr - 106 km/hr).

Seem to be the right track?
Yes. Spot on. Once you have the time, you then only need to work out how far car A has traveled in time t.

Thanks for the hint and the welcome!

For the first problem, I am assuming the acceleration is 0. Therefore, I can use the 2nd formula as delta x = (v0)t

I believe delta x of car A would be 86km/hr (t) and delta x of car B would be 106 km/hr (t). To find where they have the same displacement, I am guessing I set it up as 86km/hr (t) = 106km/h (t) + 30km
Solve for t, t = 30 km / (86km/hr - 106 km/hr).

Seem to be the right track?

Not quite: car A is the one with the 30km head start. Your "equation" has the advantage with Car B

PeterO said:
Not quite: car A is the one with the 30km head start. Your "equation" has the advantage with Car B
Good catch! I didn't spot the sign error.

## 1. How do you calculate the distance at which Car 1 overtakes Car 2?

To calculate the distance at which Car 1 overtakes Car 2, you will need to know the initial distance between the two cars, the initial speeds of both cars, and the acceleration of Car 1. Using the formula d = (v1 * t) - (v2 * t), you can find the time it takes for Car 1 to overtake Car 2. Then, using the formula d = v1 * t, you can calculate the distance at that time.

## 2. What factors affect the distance at which Car 1 overtakes Car 2?

The distance at which Car 1 overtakes Car 2 is affected by several factors, including the initial distance between the two cars, the initial speeds of both cars, the acceleration of Car 1, and any external factors such as wind or road conditions. Additionally, the mass and aerodynamics of the cars can also impact the distance at which one car overtakes the other.

## 3. Can the distance at which Car 1 overtakes Car 2 be accurately predicted?

Yes, the distance at which Car 1 overtakes Car 2 can be accurately predicted using mathematical formulas and known variables. However, it is important to note that external factors and unpredictable events can also affect the actual distance at which one car overtakes the other.

## 4. Is it possible for Car 2 to overtake Car 1?

Yes, it is possible for Car 2 to overtake Car 1 depending on the initial speeds and accelerations of both cars. If Car 2 has a higher initial speed and/or a greater acceleration, it may be able to overtake Car 1 at a certain distance.

## 5. How can the distance at which Car 1 overtakes Car 2 be used in real-life situations?

The distance at which Car 1 overtakes Car 2 can be used in real-life situations for various purposes, such as predicting the outcome of a race, determining safe passing distances on the road, and analyzing the performance of different vehicles. It can also be used to calculate the fuel efficiency of a car and make informed decisions about driving strategies and tactics.

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