Question

A train locomotive pulls a train with a mass of 1.30 ✕ 107 kg on level rails. The locomotive exerts a constant force of 6.60 ✕ 105 N on the train. How much time does it take to increase the speed of the train from rest to 74.0 km/h? (Ignore any resistance force from the rails on the wheels of the train. Enter your answer in minutes.)_____ min

Answer 1

According to Newton's Second Law of Motion, the acceleration a of an object with mass m that experiences a net force F is:

$a=\frac{F}{m}$

Replace F=6.60*10^5N and m=1.30*10^7kg to find the acceleration of the train:

$a=\frac{6.60\times10^5N}{1.30\times10^7kg}=5.077\times10^{-2}\frac{m}{s^2}$

The time t that it takes for an object with acceleration a to reach a speed v starting from rest is:

$t=\frac{v}{a}$

Replace v=74.0km/h, a=5.077*10^-2m/s^2 and convert the speed to m/s to find the time that it takes for the train to reach that speed. Convert the final answer to minutes:

$t=\frac{74.0\frac{km}{h}\times\frac{1\frac{m}{s}}{3.6\frac{km}{h}}}{5.077\times10^{-2}\frac{m}{s^2}}=404.88...s=6.748...min\approx6.75min$

Therefore, the time that it takes for the train to reach a speed of 74.0km/h is approximately 6.75 min.