Question

A train leaves the station at time t=0. Traveling at a constant speed, the train travels 420 kilometers in 2 hours. Write a function that relates the distance traveled d to the time.

Answer 1

The function which relates the distance traveled d to the time t as the train travels at a constant speed is,

$f(t)=210t,\\d=210t$

What is the speed of a body?

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

$s=\dfrac{d}{t}$

Here, (d) is the distance travelled by the body and (t) is time taken by the body to cover that distance.

A train leaves the station at time t=0. Traveling at a constant speed, the train travels 420 kilometers in 2 hours.

If the train travels 420 kilometers in 2 hours. Then by the above relation, the distance it travel in one hour will be,

$d=\dfrac{420}{2}\\d=210\rm\; km$

As the train with constant speed travels 210 km per hour. Thus the linear function for this condition can be modeled as,

$s=\dfrac{d}{t}\\210=\dfrac{d}{t}\\d=210t$

In the function of time,

$f(t)=210t$

Thus, the function which relates the distance traveled d to the time t as the train travels at a constant speed is,

$f(t)=210t,\\d=210t$

Learn more about the speed here:

https://brainly.com/question/359790