Question

A freight train has a mass of 1.5x10kg. If the locomotive can exert a constant pull of 7.5x105 N, how long would it take to increase the speed of the train from rest to 85 km/hr?

Answer 1

Given,

The mass of the train, m=1.5×10 kg=15 kg

The force with which the locomotive pulls the train, F=7.5×10⁵ N

The initial speed of the train, u=0 m/s

The final speed of the train, v=85 km/hr

The final speed in m/s is

`\begin{gathered} v=(85*1000)/(3600) \\ =23.6\text{ m/s} \end{gathered}`

From Newton's second law,

`F=ma`

Where a is the acceleration of the train.

On substituting the known values,

`\begin{gathered} 7.5*10^5=15* a \\ \Rightarrow a=(7.5*10^5)/(15) \\ =50*10^3m/s^2 \end{gathered}`

From the equation of motion,

`v=u+at`

Where t is the time interval in which the train will accelerate to the given speed.

On substituting the known values,

`\begin{gathered} 23.6=0+50*10^3* t \\ \Rightarrow t=(23.6)/(50*10^3) \\ =4.72*10^(-4)\text{ s} \end{gathered}`

Thus the train will accelerate to the given speed in 4.72×10⁻⁴ s