Suppose a train moving right at 6.0 m/s slows down at a rate of - 0.20 m/s2 until it reaches a velocity of 2.0 m/s right. How long does it take the train to undergo this change in speed?




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.

Suppose a train moving right at 6.0 m/s slows down at a rate of -0.20 m/s² until it reaches a velocity of 2.0 m/s right. How long does it take the train to undergo this change in speed?

Learn how to calculate the time it takes for a train moving at 6.0 m/s to decelerate to 2.0 m/s with an acceleration of -0.20 m/s². This problem demonstrates the first equation of motion and covers key concepts like velocity and acceleration. Suitable for Grades 9-12 physics students.

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