To calculate the acceleration, we 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 time it takes for that change.

Step 1: Convert speeds to meters per second (m/s):

Since the speeds are given in kilometers per hour (km/h), we need to convert them to meters per second (m/s).

• Initial speed: 100 km/h $100 \, \text{km/h} = \frac{100 \times 1000}{3600} \, \text{m/s} = 27.78 \, \text{m/s}$

• Final speed: 180 km/h $180 \, \text{km/h} = \frac{180 \times 1000}{3600} \, \text{m/s} = 50 \, \text{m/s}$

Step 2: Find the change in velocity:

$\Delta v = 50 \, \text{m/s} - 27.78 \, \text{m/s} = 22.22 \, \text{m/s}$

Step 3: Time taken is 1 second, so:

$a = \frac{22.22 \, \text{m/s}}{1 \, \text{s}} = 22.22 \, \text{m/s}^2$

Thus, the acceleration is 22.22 m/s².

Do you want more details or have any questions?

Here are 5 relative questions:

1. What would the acceleration be if the car took 2 seconds to reach 180 km/h?
2. How far would the car travel during that 1 second of acceleration?
3. How would braking from 180 km/h to a stop affect acceleration?
4. What is the deceleration if the car slows down from 180 km/h to 100 km/h in 5 seconds?
5. Can a typical car achieve an acceleration of 22.22 m/s²?

Tip: Acceleration is often measured in units of g, where $1g \approx 9.8 \, \text{m/s}^2$.