A rocket starts from rest and accelerates to a speed of 200 meters per second in 40 seconds.  What is its acceleration?

1. Break Down the Problem

To find the acceleration of the rocket, we need to identify the given data and the formula for acceleration. The data given includes:

• Initial speed ($u$) = 0 m/s (the rocket starts from rest)
• Final speed ($v$) = 200 m/s
• Time ($t$) = 40 s

2. Relevant Concepts

The formula to calculate acceleration ($a$) is: $a = \frac{v - u}{t}$ where:

• $v$ is the final velocity,
• $u$ is the initial velocity,
• $t$ is the time taken.

3. Analysis and Detail

Now we will substitute the known values into the acceleration formula:

• $v = 200$ m/s
• $u = 0$ m/s
• $t = 40$ s

Plugging these values into the formula gives: $a = \frac{200 \, \text{m/s} - 0 \, \text{m/s}}{40 \, \text{s}} = \frac{200 \, \text{m/s}}{40 \, \text{s}} = 5 \, \text{m/s}^2$

4. Verify and Summarize

We have calculated the acceleration as $5 \, \text{m/s}^2$. To verify, we can check if the units are consistent: meters per second squared is indeed the correct unit for acceleration, and the calculations are consistent with the formula used.

Final Answer

The acceleration of the rocket is $5 \, \text{m/s}^2$.