Constant Acc with two particles

In summary, the conversation discusses a problem involving a high-speed train and a sidecar traveling at different velocities. The question asks for the magnitude of the deceleration needed to avoid a collision. Two approaches are suggested, one involving writing positions as functions of time and solving for the minimum acceleration, and the other involving solving the motion directly using a kinematic equation.
  • #1
pappaloo
1
0
Im having a problem with this question, which is probably rather simple but I am making a lot harder than it needs to be.

A high-speed train is traveling at 44.72m/s and it sees a sidecar a distance of 676m ahead. The sidecar is traveling with a constant velocity or 8.056m/s.

The question asks what the magnitude of the resulting constant deceleration must be if a collision is to be just avoided.

I took two of the derived C.A. equations and in each one had two unknowns which were x(final) and t.

I then equated the two equations and solved the linear system for t at which I arrived with an answer of 47.26s

From there it is quite easy to figure out the rest of the question, but I am not sure if I am doing this question the best way or even correctly for that matter.

Any suggestions or comments would be greatly appreciated
 
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  • #2
I'm not sure exactly what you did, but here are two ways to approach it:
(1) Write the postions of each (sidecar and train) as a function of time. Set them equal, and solve for t. (This is what you tried, I believe.) Of course, the acceleration is a variable. Since the equation is a quadratic, you can find a constraint that will tell you the minimum acceleration that just avoids the collision.
(2) Look at the motion from the frame of the sidecar and solve it directly with a kinematic equation.

And welcome to PF!
 
  • #3
.

It seems like you are on the right track with your approach to this problem. You have correctly identified the two unknowns (x(final) and t) and used two equations to solve for them. However, there is a simpler way to approach this problem using the concept of relative velocity.

First, we can calculate the relative velocity between the train and the sidecar. This can be done by subtracting the sidecar's velocity from the train's velocity, since they are moving in the same direction. This gives us a relative velocity of 36.664m/s.

Next, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We know the initial velocity (36.664m/s) and the final velocity (0m/s, since we want the train to come to a stop just before colliding with the sidecar). We also know the distance between the train and the sidecar (676m). Plugging these values into the formula, we get:

0 = 36.664 + a(47.26)

Solving for a, we get a deceleration of -0.775m/s^2. This means that the train needs to decelerate at a rate of 0.775m/s^2 in order to avoid a collision with the sidecar.

In summary, your approach was correct, but using the concept of relative velocity can simplify the problem and give you a quicker solution. Keep up the good work!
 

1. What is meant by "Constant Acc with two particles"?

Constant acceleration with two particles refers to a scenario in which two objects are experiencing the same acceleration at all times. This could be due to a constant force acting on both objects or because they are moving in the same gravitational field.

2. How is constant acceleration calculated for two particles?

To calculate the constant acceleration for two particles, you would need to know the initial velocity, final velocity, and time interval for both particles. Using the formula a = (vf-vi)/t, you can calculate the acceleration for each particle and compare them to determine if they are experiencing the same acceleration.

3. Can two particles have different accelerations but still be considered "Constant Acc with two particles"?

No, for two particles to be considered "Constant Acc", they must have the same acceleration at all times. If the accelerations are different, the objects are not experiencing constant acceleration and the situation would be considered non-uniform motion.

4. How does air resistance affect "Constant Acc with two particles"?

In a vacuum or in the absence of air resistance, two particles experiencing the same acceleration would continue to have the same acceleration. However, in the presence of air resistance, the particles may experience different accelerations due to differences in their masses, surface areas, and velocities.

5. What are some real-life examples of "Constant Acc with two particles"?

Some real-life examples of "Constant Acc with two particles" include a car and a passenger inside the car, both experiencing the same acceleration as the car moves forward, or two objects falling towards the ground with the same acceleration due to gravity.

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