Question

create a problem that has you find the acceleration of something

Answer 1

**Problem:**

A car accelerates uniformly from rest to a speed of 25 meters per second (m/s) in 10 seconds.

**Questions:**
1. What is the acceleration of the car?
2. How far did the car travel during this time?

**Solution:**

1. **Finding the Acceleration:**

The formula for acceleration (\(a\)) when starting from rest is given by:

\[
a = \frac{\Delta v}{\Delta t}
\]

Where:
- \(\Delta v\) is the change in velocity,
- \(\Delta t\) is the change in time.

Given:
- Initial velocity (\(v_0\)) = 0 m/s (starting from rest)
- Final velocity (\(v_f\)) = 25 m/s
- Change in time (\(\Delta t\)) = 10 s

Thus, the change in velocity (\(\Delta v\)) is:

\[
\Delta v = v_f - v_0 = 25 \, \text{m/s} - 0 \, \text{m/s} = 25 \, \text{m/s}
\]

Now, substituting the values into the acceleration formula:

\[
a = \frac{25 \, \text{m/s}}{10 \, \text{s}} = 2.5 \, \text{m/s}^2
\]

**Accelerations of the car is 2.5 m/s².**

2. **Finding the Distance Traveled:**

The formula for distance (\(d\)) traveled under uniform acceleration from rest is given by:

\[
d = v_0 \Delta t + \frac{1}{2} a (\Delta t)^2
\]

Substituting the known values:

- \(v_0 = 0\) (the initial velocity)
- \(a = 2.5 \, \text{m/s}^2\)
- \(\Delta t = 10 \, \text{s}\)

We get:

\[
d = 0 + \frac{1}{2} \times 2.5 \, \text{m/s}^2 \times (10 \, \text{s})^2
\]
\[
d = \frac{1}{2} \times 2.5 \, \text{m/s}^2 \times 100 \, \text{s}^2
\]
\[
d = 1.25 \times 100 = 125 \, \text{m}
\]

**The car traveled 125 meters during this time.**

**Final Answers:**
- Acceleration: \(2.5 \, \text{m/s}^2\)
- Distance Traveled: \(125 \, \text{m}\)