# Help In understanding Rate Of Change in mm per sec

• tomtomtom1
= (25 mm x 136.794) / 216 sec= (25 mm x 136.794) / (3.6 x 60 x 1) sec= (25 mm x 136.794) / (3.6 x 60 x (1000/1000)) sec= (25 mm x 136.794) / (3.6 x 60 x (1000/1000)) sec= (25 mm x 136.794) / (3.6 x 60 x 1000) sec= (25 mm x 136.794) / 360000 sec= (25 mm) x (136.794/360000

#### tomtomtom1

Hi everyone

Firstly this is not a homework question, i work in transport engineering. ( i do study part time which is why i sometimes post in the homework section)

Now to the problem.

I am trying to understand how to solve this problem, i already know the answer.

A train is traveling on straight & level track at 136.794kph.
It approaches a transition. The transition is 60m long.
Along the transition the Left Rail rises linearly over the length of the transition relative to the right Rail by 25mm.
Calculate the rate of change the left rail raises over the right in mm per sec over the 60m transition at 136.794kph.

i know that the answer is (25mm * 136.794kph) / (3.6 * 60m)

what i need help with is where does the 3.6 some from? and why do you times 25mm by 136.794kph?

can anyone explain

Thanks

The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?
The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?

The transition length is 60 m long. In this distance, the rails rise by 25 mm. Doesn't this suggest a slope?

Yes there is a slope and the slope is 25mm/60m = 1m per 0.416mm which means for every 1m the train travels along the transition the left rail rises by 0.416mm.

The train is traveling at 136.794 km/hr. How do you convert 136.794 km/hr to a speed measured in m/s?

1kph = 0.277777778 m/s so 136.794km/hr in m/s is 136.794*0.277777778 = 37.998m/s.

rate of change the left rail raises = 25mm / (time needed to cross 60m)
= 25 mm / (60 m / velocity)
= 25 mm / (60 m / 136.794 km per hour)
Now, 1 km per hour = 1000 m / 3600 sec = 1/3.6 meter per sec
So,
rate of raise = 25 mm / (60 m / ((136.794 / 3.6) meter per sec))
= 25 mm / (3.6 x 60 / 136.794) sec
= (25 mm x 136.794) / (3.6 x 60) sec

## What is the definition of rate of change in mm per sec?

The rate of change in mm per sec refers to the measurement of how quickly a quantity is changing over a specific period of time, specifically in terms of millimeters per second. It is a measure of the slope or steepness of a line on a graph.

## Why is understanding rate of change important in scientific research?

Understanding rate of change is important in scientific research because it allows scientists to analyze and compare data, make predictions, and identify trends. It also helps in determining the relationships between different variables and can provide valuable insights into various physical processes.

## How is rate of change calculated?

The rate of change is calculated by dividing the change in the quantity of interest by the time interval over which the change occurred. This is represented by the formula: rate of change = (final value - initial value) / time interval.

## What are some real-world examples of rate of change in mm per sec?

Some real-world examples of rate of change in mm per sec include measuring the speed of an object in motion, calculating the growth rate of a plant or animal, and analyzing the flow rate of a liquid or gas. It can also be used to study changes in weather patterns or the movement of tectonic plates.

## How can rate of change be graphically represented?

Rate of change can be graphically represented by plotting the data points on a graph and drawing a line connecting them. The slope of the line represents the rate of change, with a steeper slope indicating a higher rate of change and a flatter slope indicating a lower rate of change. This visual representation makes it easier to understand and analyze the data.