The question from the image is about the motion of a train with an initial acceleration followed by deceleration until it stops. Here's a breakdown:

Given:

• Initial acceleration: $2 \, \text{m/s}^2$ for some time.
• Final deceleration: $4 \, \text{m/s}^2$ until the train comes to a stop.
• Initial condition: The train starts from rest.

The question asks for the total distance traveled by the train.

Key Steps to Solve:

1. Calculate the velocity after acceleration phase:

   • Using the equation $v = u + at$ where:
     • $u = 0 \, \text{m/s}$ (starts from rest),
     • $a = 2 \, \text{m/s}^2$ (acceleration),
     • $t = \text{time of acceleration phase}$.

2. Calculate the stopping distance during deceleration:

   • Using the equation $v^2 = u^2 + 2as$, where:
     • $u$ is the velocity at the end of acceleration,
     • $a = -4 \, \text{m/s}^2$ (deceleration),
     • $v = 0 \, \text{m/s}$ (final velocity when stopped),
     • $s$ is the stopping distance.

3. Add both distances to find the total distance traveled.

Would you like me to complete the calculations step by step?

Related Questions:

1. What is the formula for uniformly accelerated motion?
2. How does deceleration affect motion equations?
3. What other variables would affect the total stopping distance?
4. Can the total distance traveled be found using energy conservation?
5. How do different acceleration rates change the overall journey?

Tip:

Always keep track of whether you're dealing with acceleration or deceleration, as they influence motion in opposite directions.