Question

A train is traveling down a straight track at 26 m/s when the engineer applies the brakes, resulting in an acceleration of −1.0 m/s2 as long as the train is in motion. How far does the train move during a 52-s time interval starting at the instant the brakes are applied?______ m

Answer 1

In order to calculate the distance the train will move, we can use the formula below:

`\Delta S=V_0t+(at^2)/(2)`

Where V0 is the initial speed, t is the time and a is the acceleration.

Since the initial speed is 26 m/s and the train acceleration is -1 m/s², the train will completely stop after 26 seconds. In the remaining 26 seconds to complete the total of 52, the train will be stopped already, so there is no displacement.

Because of that, we will use a time t = 26 seconds.

So, using V0 = 26 m/s and a = -1 m/s², we have:

`\begin{gathered} \Delta S=26\cdot26+((-1)26^2)/(2)\\ \\ \Delta S=676-338\\ \\ \Delta S=338\text{ m} \end{gathered}`

Therefore the train will move 338 meters.