Tag Archives: time for a runaway train car to stop

College Physics by Openstax Chapter 8 Problem 5

A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. Compute the time required for a force of 1500 N to bring the car to rest.

Solution:

Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes. In symbols, Newton’s second law of motion is defined to be

Fnet=ΔpΔt,\textbf{F}_{\text{net}} = \frac{\Delta \textbf{p}}{\Delta t} ,

where Fnet\textbf{F}_{\text{net}} is the net external force, Δp\Delta \textbf{p} is the change in momentum, and Δt\Delta t is the change in time.

For this problem, we are given the following values:

m=15000 kgvinitial=5.4 m/svfinal=0 m/sFnet=1500 N\begin{align*} m & = 15000\ \text{kg} \\ \textbf{v}_{\text{initial}} & = 5.4\ \text{m}/\text{s} \\ \textbf{v}_{\text{final}} & = 0\ \text{m}/\text{s} \\ \textbf{F}_{\text{net}} & = 1500\ \text{N} \end{align*}

Substitute these given values in the equation above.

Fnet=ΔpΔtΔt=ΔpFnetΔt=m(Δv)FnetΔt=15000 kg(5.4 m/s)1500 NΔt=54 s  (Answer)\begin{align*} \textbf{F}_{\text{net}} & = \frac{\Delta \textbf{p}}{\Delta t} \\ \Delta t & = \frac{\Delta \textbf{p}}{\textbf{F}_{\text{net}}} \\ \Delta t & = \frac{m \left( \Delta\textbf{v} \right)}{\textbf{F}_{\text{net}}} \\ \Delta t & = \frac{15000\ \text{kg} \left( 5.4\ \text{m}/\text{s} \right)}{1500\ \text{N}} \\ \Delta t & = 54\ s \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}

It would take 54 seconds to stop the car.