Question

The wheels of the locomotive push back on the tracks with a constant net force of 7.50 × 105 N, so the tracks push forward on the locomotive with a force of the same magnitude. Ignore aerodynamics and friction on the other wheels of the train. How long, in seconds, would it take to increase the speed of the train from rest to 80.0 km/h?

Answer 1

The freight train would take 542.265 second to increase the speed of the train from rest to 80.0 kilometers per hour.

Step-by-step explanation:

Statement is incomplete. Complete description is presented below:

A freight train has a mass of
`1.83* 10^(7)\,kg`. The wheels of the locomotive push back on the tracks with a constant net force of
`7.50* 10^(5)\,N`, so the tracks push forward on the locomotive with a force of the same magnitude. Ignore aerodynamics and friction on the other wheels of the train. How long, in seconds, would it take to increase the speed of the train from rest to 80.0 kilometers per hour?

If locomotive have a constant net force (
`F`), measured in newtons, then acceleration (
`a`), measured in meters per square second, must be constant and can be found by the following expression:

`a = (F)/(m)` (1)

Where
`m` is the mass of the freight train, measured in kilograms.

If we know that
`F = 7.50* 10^(5)\,N` and
`m = 1.83* 10^(7)\,kg`, then the acceleration experimented by the train is:

`a = (7.50* 10^(5)\,N)/(1.83* 10^(7)\,kg)`

`a = 4.098* 10^(-2)\,(m)/(s^(2))`

Now, the time taken to accelerate the freight train from rest (
`t`), measured in seconds, is determined by the following formula:

`t = (v-v_(o))/(a)` (2)

Where:

`v` - Final speed of the train, measured in meters per second.

`v_(o)` - Initial speed of the train, measured in meters per second.

If we know that
`a = 4.098* 10^(-2)\,(m)/(s^(2))`,
`v_(o) = 0\,(m)/(s)` and
`v = 22.222\,(m)/(s)`, the time taken by the freight train is:

`t = (22.222\,(m)/(s)-0\,(m)/(s) )/(4.098* 10^(-2)\,(m)/(s^(2)) )`

`t = 542.265\,s`

The freight train would take 542.265 second to increase the speed of the train from rest to 80.0 kilometers per hour.