Solving Complex Math Problems: Deceleration, Acceleration, & Earthquakes

In summary, we have two problems to solve. The first one involves calculating the time lost due to a train stopping at a station, using the train's deceleration and acceleration rates. The second problem requires finding the speed and time elapsed of a pickup truck that applies brakes and decelerates over a distance. Lastly, the third problem involves finding the distance between a seismograph and the center of an earthquake using the arrival times of transverse and longitudinal seismic waves.
  • #1
BriannaUND
12
0
i don't know why I'm having so many problems but I greatly appreciate the help!
1) A train normally travels at a uniform speed of 72 km/hr on a long stretch of straight, level track. On a particular day, the train must make a 2.0-min stop at a station along this track. If the train decelerates at a uniform rate of 1.0m/s2 and, after the stop, accelerates at a rate of .5 m/s2, how much time is lost because of stopping at the station?
So far I have calculated vo= 72 km/hr (.278 m/s divided by 1 km/hr) = 20.0 m/s. Then t= v-vo/a = 0-20 m/s divided by -1.0 m/s2 = 20 sec to stop. Does this look correct? And how do I go about calculating the time lost?
2)The driver of a pickup truck going 100 km/hr applies the brakes, giving the truck a uniform deceleration of 6.5 m/s2 while it travels 20.0 m. a) what is the speed of the truck in km/hr at the end of this distance? and b) how much time has elapsed?
3) An earthquake releases two types of traveling waves, called transverse and longitudinal. The average speeds of transverse and longitudinal seismic waves in rock are 8.9 km/s and 5.1 km/s respectively. A seismograph records the arrival of the transverse waves 73 s before that of the longitudinal waves. Assuming that the waves travel in straight lines, how far away is the center of the earthquake from the seismograph?
Thanks again!
 
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  • #2
You don't seem to have put much effort into this.

So far, 1) is perfect. Think, and keep going.

2) & 3) Yeah, so what are your thoughts on how to tackle these problems?


P.S. Please post further threads in the homework section: https://www.physicsforums.com/forumdisplay.php?f=15. Thanks.
 
Last edited:
  • #3
As for
#2a) I've calculated v2 = 100 km/hr + 2 (-6.5 m/s2)(20 m), v2 = 360, v= 18.9, 100-18.9 = 81.1 km/hr
#2b) vx= vox + axt making 81.1 = 100 + (-6.5)t making t= 2.9 sec
#3) I've tried calculating average velocity and then plugging that answer in for x= average velocity x time for both of the waves. But I'm getting confused because the problem states that the arrival of the t-waves "73 sec before l-waves" so I'm not sure what to plug in for t when calculating the distance of the l-waves
 
  • #4
#2a is wrong. So #2b is also wrong. You are on the right track but your calculation is wrong.
[tex]v_f ^ 2 = v_i ^ 2 + 2ad[/tex]. You should also convert the 100 km / h to m / s.
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The transverse waves is faster than the longitudinal waves, therefore the transverse waves will reach the seismograph before the longitudinal waves (73 sec before the l-waves).
The two types of waves are released at the same time. If it takes the t-waves t (seconds) to reach the seismograph, then it takes the l-waves t + 73 seconds to reach the seismograph. So you have the time each kind of waves need to reach the seismograph. To reach the seismograph, they travels the same distance. So:
[tex]v_l (t + 73) = v_t t[/tex]
You know the v_l : speed of l-waves, v_t : speed of t-waves. You can find the amount of time (t) it takes the t-waves to reach the seismograph. From there, you can easily find the distance from the seismograph to the center of the earthquake.
Viet Dao,
 

1. What is the difference between deceleration and acceleration?

Deceleration refers to a decrease in speed or velocity, while acceleration refers to an increase in speed or velocity. Deceleration is often represented with a negative value, while acceleration is represented with a positive value.

2. How do you calculate deceleration and acceleration?

To calculate deceleration or acceleration, you need to know the initial velocity, final velocity, and time. The formula for calculating deceleration is (final velocity - initial velocity)/time, while the formula for acceleration is (final velocity - initial velocity)/time.

3. What is the role of deceleration and acceleration in solving complex math problems?

Deceleration and acceleration are important concepts in physics and are often used to describe the motion of objects. They can be applied to solve complex math problems involving motion, such as calculating the distance traveled or time taken for an object to reach a certain speed.

4. How are deceleration and acceleration related to earthquakes?

Earthquakes are a result of the movement of tectonic plates, which can cause deceleration and acceleration of the Earth's crust. Deceleration occurs when the plates are moving away from each other, while acceleration occurs when the plates are moving towards each other.

5. Can deceleration and acceleration be measured during an earthquake?

Yes, deceleration and acceleration during an earthquake can be measured using devices called seismometers. These instruments record the ground motion caused by the movement of tectonic plates and can provide valuable data for understanding and predicting earthquakes.

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