To determine how long it takes the train to change its speed, we can use the first equation of motion:

$v = u + at$

Where:

• $v$ is the final velocity (2.0 m/s),
• $u$ is the initial velocity (6.0 m/s),
• $a$ is the acceleration (-0.20 m/s²),
• $t$ is the time we are trying to find.

We can rearrange the equation to solve for time ($t$):

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

Now substitute the given values:

$t = \frac{2.0 \, \text{m/s} - 6.0 \, \text{m/s}}{-0.20 \, \text{m/s}^2}$

$t = \frac{-4.0}{-0.20} = 20 \, \text{seconds}$

So, it takes 20 seconds for the train to slow down from 6.0 m/s to 2.0 m/s.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What is the distance covered by the train during this deceleration?
2. How would the time change if the acceleration were -0.40 m/s²?
3. If the train were moving left instead of right, how would that affect the calculations?
4. How long would it take for the train to come to a complete stop?
5. What is the significance of negative acceleration in this context?

Tip: Always pay attention to the signs (positive or negative) when dealing with velocity and acceleration in problems involving direction.