# Calculating Train Speed Increase: 1.5x10^7 kg Train

• Jordash
You could use the equation v = u + at, where u is the initial velocity, v is the final velocity, a is the acceleration, and t is the time. Since the train starts from rest, u = 0. You can rearrange the equation to solve for t, and plug in the values of a and v to find the time it takes for the train to reach 80km/h. In summary, the conversation discusses the calculation of the time it would take for a freight train with a mass of 1.5x10^7 kg to increase its speed from rest to 80km/h, given a constant net force of 7.5x10^5N pushing back on the tracks. The suggested
Jordash

## Homework Statement

A frieght train has a mass of 1.5x10^7 kg. The wheels of the locomotive push back on the tracks with a constant net force of 7.5X10^5N, so the tracks push forward on the locomotive with a force of equal magnitude. (ignore aerodynamics and friction) how long would it take to increase the speed of the train from rest to 80km/h?

## The Attempt at a Solution

So far I was able to calculate the acceleration:

a=F/m

a=7.5*10^5/1.5*10^7

a=5*10^12m/s^2

am I going in the right direction and how would I proceed?

I believe you are on the right track. You need to use one of the kinematics equation though to find the time.

I would approach this problem by using the equation for acceleration, a=F/m, which you have correctly identified. From there, I would use the equation for average velocity, v=at, where v is the final velocity, a is the acceleration, and t is the time. In this case, we are looking for the time it takes for the train to reach a final velocity of 80 km/h, which we can convert to meters per second by multiplying by 1000/3600, giving us 22.22 m/s. Plugging in our known values for acceleration and final velocity, we get:

22.22 m/s = (5*10^12 m/s^2)t

Solving for t, we get t = 4.44*10^-12 seconds.

However, this answer may not be realistic as it does not take into account the limitations of the train's engine and the track's ability to withstand such high forces. It is important to consider the practicality and feasibility of the solution in addition to the mathematical calculations.

## 1. How is train speed increase calculated?

The formula for calculating train speed increase is: Speed Increase = (New Train Mass - Original Train Mass) / Original Train Mass * 100%

## 2. What is the mass of the train?

The mass of the train is 1.5x10^7 kg.

## 3. How do you convert from kg to metric tons?

To convert from kg to metric tons, divide the mass by 1000. In this case, the train's mass in metric tons would be 1.5x10^4 metric tons.

## 4. How does the train's mass affect its speed?

The train's mass directly affects its speed. The heavier the train, the more force is needed to accelerate it, thus decreasing its speed. In contrast, a lighter train would require less force and can achieve a higher speed.

## 5. How can train speed increase be measured in real life?

Train speed increase can be measured by using speedometers or GPS systems on the train. The speed can be recorded before and after the increase and the difference can be calculated to determine the speed increase.

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