# Solve Constant Velocity: Dogs Collision in 85m

• baileya
In summary: So in this equation x=vt and t=0 so it would be saying that the first dog is at x=85 and the second dog is at x=-85.In summary, Homework Equations state that the position of an object is a function of its velocity and time. When time equals to zero, x2=85.
baileya

## Homework Statement

Two dogs stand facing each other 85 meters apart. They begin to run towards each other. Dog A runs at a constant velocity of 3.5 m/s; Dog B is going the opposite direction at a constant -2.8 m/s. How long before the dogs collide?

## Homework Equations

Xfinal-Xinitial = vt

## The Attempt at a Solution

I looked through my notes from class and tried to work through it. I also googled it but couldn't figure it out.

Write out your two equations of motion.

For dog 1 you would simply have x(t)=3.5t if you choose him to be at zero on your coordinate axis.

For dog 2 what would you have?

Once you set those two position functions equal to each other you will be able to solve for the time. Then simply plug that time into either of the two functions and they will provide the same result of where the dogs collide.

haha this probably makes me sound really stupid but you're going to have to explain it in more simple terms... if that's possible.

I just really don't get this question.

Okay, so you have learned that position i will call it 'x' is equal to velocity multiplied by time or x=vt for motion in 1-D. What this really means is that given some velocity
'v' you substitute in any value for time 't' (greater than zero since time can't be negative) and get the position of whatever object at that chosen time. So it really means that position is your dependent variable and time is your independent variable...or position is a function of time written as x(t).

The second position function is a little trickier than just x2=-2.8t because it doesn't start at x=0 it starts at x=85m (since i choose the first dog to be at zero and the dogs are 85m apart). If you were to sub zero in for time in the equation above you would get that x2=0 which is incorrect. So you need to add a constant that when time equals to zero makes x2=85...

Pretty much all you are dealing with is functions just like what was covered in algebra when you discussed lines often given the general formula y=mx+b

I would approach this problem by first defining the variables and units involved. In this case, the distance between the dogs is 85 meters, the velocity of Dog A is 3.5 m/s and the velocity of Dog B is -2.8 m/s. The negative sign for Dog B's velocity indicates that it is moving in the opposite direction.

Next, I would use the formula Xfinal-Xinitial = vt to calculate the time it takes for the dogs to collide. In this formula, Xfinal represents the final position of the dogs, Xinitial represents their initial positions, v represents their velocities, and t represents time.

Using this formula, we can set up two equations:

For Dog A: Xfinal = 85 meters, Xinitial = 0 meters, v = 3.5 m/s
For Dog B: Xfinal = 0 meters, Xinitial = 85 meters, v = -2.8 m/s

Plugging these values into the formula, we get:

85 - 0 = 3.5t for Dog A
0 - 85 = -2.8t for Dog B

Solving for t in both equations, we get t = 24.29 seconds for Dog A and t = 30.36 seconds for Dog B.

Since we are looking for the time it takes for the dogs to collide, we can use the average of these two values, which is t = 27.33 seconds.

Therefore, it will take approximately 27.33 seconds for the dogs to collide.

## 1. How do you calculate the constant velocity of two dogs colliding in 85m?

To calculate the constant velocity, we use the formula v=d/t, where v is the velocity in m/s, d is the distance in meters, and t is the time in seconds. In this case, we know that the distance is 85m and we can measure the time it takes for the dogs to collide. Plug in those values into the formula to calculate the constant velocity.

## 2. What factors can affect the constant velocity of the dogs' collision?

The constant velocity of the dogs' collision can be affected by factors such as the mass and speed of the dogs, any external forces acting on the dogs, and the surface they are colliding on. These factors can change the acceleration and therefore the velocity of the dogs.

## 3. What is the significance of finding the constant velocity of the dogs' collision?

Finding the constant velocity of the dogs' collision can help us understand the physical laws that govern their movement. It can also help us make predictions about how the dogs will move and interact in future collisions.

## 4. How does the constant velocity of the dogs' collision differ from the average velocity?

The constant velocity of the dogs' collision is the velocity at a specific moment in time, while the average velocity is the total distance traveled divided by the total time taken. The constant velocity only considers the velocity at the point of collision, while the average velocity takes into account the entire duration of the dogs' movement.

## 5. Can the constant velocity of the dogs' collision be negative?

Yes, the constant velocity of the dogs' collision can be negative if the dogs are moving in opposite directions or if they have a negative acceleration. A negative velocity indicates that the dogs are moving in the opposite direction of the chosen coordinate system.

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