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
\textbf{F}_{\text{net}} = \frac{\Delta \textbf{p}}{\Delta t} ,
where \textbf{F}_{\text{net}} is the net external force, \Delta \textbf{p} is the change in momentum, and \Delta t is the change in time.
For this problem, we are given the following values:
\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.
\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.