A train on a straight stretch of track starts from rest and accelerates at a steady 2 m/s/s. Determine its speed after 1 second, 2 seconds, and 5 seconds.

1. ### Break Down the Problem

To find the speed of the train at different times, we will use the formula for acceleration: $v = u + at$ where:

• $v$ = final velocity (speed)
• $u$ = initial velocity (0 m/s since it starts from rest)
• $a$ = acceleration (2 m/s²)
• $t$ = time in seconds

We need to calculate the speed after 1 second, 2 seconds, and 5 seconds.

2. ### Relevant Concepts

Using the formula: $v = 0 + (2 \, \text{m/s}^2 \cdot t)$ So, we will substitute $t$ with 1, 2, and 5 seconds respectively.

3. ### Analysis and Detail

1. After 1 second: $v = 2 \, \text{m/s}^2 \cdot 1 \, \text{s} = 2 \, \text{m/s}$

2. After 2 seconds: $v = 2 \, \text{m/s}^2 \cdot 2 \, \text{s} = 4 \, \text{m/s}$

3. After 5 seconds: $v = 2 \, \text{m/s}^2 \cdot 5 \, \text{s} = 10 \, \text{m/s}$

4. ### Verify and Summarize

The calculations for each time interval have been performed using the acceleration formula. The results are consistent with the physics of motion under constant acceleration.

Final Answer

• Speed after 1 second: 2 m/s
• Speed after 2 seconds: 4 m/s
• Speed after 5 seconds: 10 m/s