Running at a speed of $60\text{km/h}$, a train passed through a $1.5\text{km}$ long tunnel in $2\text{minutes}$. What is the length of the train?

Let's convert the given parameters to standard metric units ($\text{m/s}$ and seconds):
1. Convert speed:

$$v=60\text{km/h}=60\times \frac{5}{18}\text{m/s}=\frac{50}{3}\text{m/s}$$

2. Convert time:

$$t=2\text{minutes}=2\times 60\text{seconds}=120\text{seconds}$$

3. Calculate total distance covered:

$$\text{Total Distance}=\text{speed}\times \text{time}=\frac{50}{3}\times 120=50\times 40=2000\text{m}$$

4. Determine train length:
The total distance is equal to the length of the tunnel plus the length of the train.

$$\text{Tunnel length}=1.5\text{km}=1500\text{m}$$

$$\text{Length of the train}=\text{Total Distance}-\text{Tunnel length}$$

$$\text{Length of the train}=2000\text{m}-1500\text{m}=500\text{m}$$