Question

A car accelerates from 20 km/h to 80 km/h in 8 seconds. Find the acceleration of the car and provide step-by-step calculations to support the answer.

Answer 1

To find the acceleration of the car, we can use the formula for acceleration:

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

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

### Step 1: Convert the velocities to a consistent unit
First, we'll convert the velocities from kilometers per hour (km/h) to meters per second (m/s). The conversion factor is:

\[
1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}
\]

- Initial velocity (\(v_i\)):
\(20 \, \text{km/h} = 20 \div 3.6 \approx 5.56 \, \text{m/s}\)

- Final velocity (\(v_f\)):
\(80 \, \text{km/h} = 80 \div 3.6 \approx 22.22 \, \text{m/s}\)

### Step 2: Calculate the change in velocity
Now, we calculate the change in velocity (\(\Delta v\)):

\[
\Delta v = v_f - v_i = 22.22 \, \text{m/s} - 5.56 \, \text{m/s} \approx 16.66 \, \text{m/s}
\]

### Step 3: Determine the change in time
The change in time (\(\Delta t\)) is given as:

\[
\Delta t = 8 \text{ seconds}
\]

### Step 4: Calculate acceleration
Now we can plug the values into the acceleration formula:

\[
a = \frac{\Delta v}{\Delta t} = \frac{16.66 \, \text{m/s}}{8 \, \text{s}} \approx 2.08 \, \text{m/s}^2
\]

### Conclusion
The acceleration of the car is approximately:

\[
\boxed{2.08 \, \text{m/s}^2}
\]