How Is Velocity Calculated in Physics Problems?

[xkrazaylaught]

Hi everybody,

I had 2 HW questions that I didn't get for my physics class, and I would really appreciated if you could explain them to me. They're pretty simple, I think, but the way they're worded makes it difficult to picture.

1) Two trains, each having a speed of 30 km/hr, are headed at each other on the same straight track. A bird that can fly 60 k /hr flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. ( We have no idea why a bird would behave this way). What is the total distance the bird travels?

2) If a particle's position is given by x= 4mp - (12m/s)t+(3 m/s^2)(t^2), what is its velocity at t1 = 1 s?

For this problem, the correct answer is -6m/s (answers on the back of the book) but I don't know how to get that.


Thank you so much for your time!

 

[Kalvarin]

Imagine it like this, there is a gap between the trains that gets smaller and smaller until they collide. The bird can keep flying in this gap until the trains collide, when they collide there is no gap and so the bird can't fly anymore. We know how fast the bird can fly, so if we can work out how long it is able to fly in the gap we can work out how far it has travelled. So we need to calculate how long the gap exists for, or in other words at what point in time the trains will collide. Once you work out the timeyou can work out how far the bird was able to fly, because we know how fast the bird was flying :)

For the second question you need to use calculus. Remember that dx/dt, the change in distance with respect to time, gives us velocity? You should be able to work it out from that.

 

[tomcue]

Hello,

I am happy to help explain these questions to you. Let's start with the first one about the bird flying between two trains. This is an example of relative motion, meaning that the motion of the bird is relative to the motion of the trains. Since the trains are moving towards each other at the same speed, the distance between them is decreasing at a rate of 60 km/hr (30 km/hr + 30 km/hr). This means that the bird is essentially flying back and forth between two points that are getting closer together at a constant rate. Therefore, the total distance the bird travels can be calculated by multiplying the bird's speed (60 km/hr) by the time it takes for the trains to collide, which is 60 km / 60 km/hr = 1 hour. So the bird travels a total distance of 60 km.

Now for the second question, we can use the equation for velocity, which is the derivative of position with respect to time. In this case, the particle's position is given by x = 4mp - 12m/s*t + 3m/s^2*(t^2). Taking the derivative with respect to time, we get the velocity equation v = -12m/s + 6m/s^2*t. Plugging in t = 1 s, we get v = -12m/s + 6m/s^2*1 s = -6m/s. This is the velocity at t1 = 1 s. I hope this helps you understand the problems better. Let me know if you have any further questions.