Example: Train A train moves, starting from rest with an acceleration of $$ 2 \mathrm{~m} / \mathrm{s}^{2} $$ along a straight road. 1. What is its speed (instantaneous) after 6 seconds? Starts from rest means $$ v_{0}=0 . \quad v=v_{0}+a t=0+2 \frac{\mathrm{~m}}{\mathrm{~s}^{2}} imes 6 \mathrm{~s}=12 \frac{\mathrm{~m}}{\mathrm{~s}} $$

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Example: Train A train moves, starting from rest with an acceleration of $$ 2 \mathrm{~m} / \mathrm{s}^{2} $$ along a straight road. 1. What is its speed (instantaneous) after 6 seconds? Starts from rest means $$ v_{0}=0 . \quad v=v_{0}+a t=0+2 \frac{\mathrm{~m}}{\mathrm{~s}^{2}} 	imes 6 \mathrm{~s}=12 \frac{\mathrm{~m}}{\mathrm{~s}} $$

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Let's break down the problem step by step.

### Known Conditions:
- Initial speed $$ v_0 = 0 \, \mathrm{m/s} $$ (the train starts from rest)
- Acceleration $$ a = 2 \, \mathrm{m/s}^2 $$
- Time $$ t = 6 \, \mathrm{s} $$

### Step-by-Step Solution:
1. **Identify the formula for final velocity**:
   The formula to calculate the final velocity $$ v $$ when starting from rest is:
   $$
   v = v_0 + a t
   $$

2. **Substitute the known values into the formula**:
   Since $$ v_0 = 0 $$, the equation simplifies to:
   $$
   v = 0 + 2 \, \mathrm{m/s}^2 \times 6 \, \mathrm{s}
   $$

3. **Perform the multiplication**:
   $$
   v = 2 \times 6 = 12 \, \mathrm{m/s}
   $$

### Final Answer:
The instantaneous speed of the train after 6 seconds is $$ 12 \, \mathrm{m/s} $$.
After 6 seconds, the train is moving at 12 meters per second.

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