When and Where Do Two Cars Collide? A Velocity Analysis

In summary, two cars are initially at rest, with Car A at x=2500m and Car B at x=-1000m. At t=5s, Car A starts moving at a constant velocity of 25 m/s in the positive x direction, while at the same time Car B starts moving at a constant velocity of 30 m/s in the positive x direction. The question is when and where will the two cars collide. To solve this problem, you will need to set two equations equal to each other, one that relates distance traveled to speed and time, and one that takes into account the initial positions of the cars. With this information, you can find the time at which the two cars collide and the position at
  • #1
aziegler@uark
2
0

Homework Statement


Two cars are at rest. Car A is at x=2500m, and Car B is at x=-1000m. At t=5s car A instantly travels at a constant velocity of 25 m/s in the positive x direction. At the same time car A takes off, car B travels at a constant velocity of 30 m/s, also in the positive x direction. When does car B collide with car A? Where does this occur?


Homework Equations


velocity=displacement/time; speed=distance traveled/time;


The Attempt at a Solution

I am having trouble with this problem 1. because I have never taken physics and 2. because its wording is confusing me a bit. I tried to make a graph of this problem, but I thought that time is usually the x-axis and position is usually the y-axis, but the problem says that the cars' positions are on the x-axis and the time I guess would be the y-axis. I think I need to set two equations equal to each other and solve for the variable time, but I'm having trouble finding a starting point. I have to stopping point so I can't figure out a ratio of the two either. Please help!
 
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  • #2
You will need to set two equations equal to each other. When the cars collide their positions will be the same. You need an equation that relates the distance traveled to the speed they're traveling and the time. Also do not forget they do not start at the origin (or 0).
 
  • #3
Thanks Kurdt! I will try this out and play with the numbers.
 

Related to When and Where Do Two Cars Collide? A Velocity Analysis

1. What is velocity and how is it calculated?

Velocity is a measure of the rate of change of an object's position. It is calculated by dividing the change in position by the change in time. The formula for velocity is v = Δx/Δt, where v is velocity, Δx is change in position, and Δt is change in time.

2. How does the velocity of two colliding cars affect the collision?

The velocity of two colliding cars determines the severity of the collision. The higher the velocity of the cars, the greater the force of impact and the more damage that is likely to occur. This is why it is important to follow speed limits and drive at safe velocities.

3. Can the velocity of a car change during a collision?

Yes, the velocity of a car can change during a collision. This is due to the conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force. Therefore, during a collision, the velocities of the cars involved may change depending on the masses and velocities of each car.

4. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have different meanings in physics. Velocity is a vector quantity that includes both magnitude (speed) and direction, while speed is a scalar quantity that only measures magnitude. In other words, velocity tells us not only how fast an object is moving, but also in what direction.

5. How can velocity be used to determine the outcome of a car collision?

Velocity can be used to determine the outcome of a car collision by calculating the momentum of each car before and after the collision. The change in momentum, along with the mass of the cars, can help determine the force of impact and the severity of the collision. This information can be used to assess the safety of vehicles and improve car designs to make them more crash-resistant.

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