Question

A train whose weight is 16 metric tons, moves at the rate of 72 kmph. After applying brakes it stops in 500 meters. What is the force executed by brakes?

• A. 600 N
• B. 1600 N
• C. 3200 N
• D. 6400 N

Answer 1

The Correct Option is D

To calculate the force exerted by the brakes, you can use the following formula:
Force (F) = (Mass\(\times\)Acceleration)
First, convert the speed from km/h to m/s:
Speed in \((\frac{m}{s})=\frac{(\frac{72km}{h})\times(\frac{1000m}{km})}{(\frac{3600s}{h})}=\frac{20m}{s}\)
The acceleration (a) can be calculated using the formula:
Acceleration \((a)=\frac{(Change in Velocity)}{(Time)}\)
The change in velocity is the initial velocity (0 \(\frac{m}{s}\) because the train is stopping) minus the final velocity \((\frac{20m}{s})\).
The time (t) is given as the distance (500 meters) divided by the speed \((\frac{20m}{s})\):
\(a=\frac{(\frac{0m}{s}-\frac{20m}{s})}{(\frac{500m}{\frac{20m}{s}})}\)\(=\frac{(\frac{-20m}{s})}{(25s)}=\frac{-0.8m}{s^2}\)
Now, you can calculate the force (F):
F =(Mass\(\times\)Acceleration) = (16,000 kg\(\times\)(-0.8 m/s²)) =-12,800 N
The negative sign indicates that the force is acting in the opposite direction of motion (braking force). 
So, the correct answer is: (4) 6400 N