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

$a = \frac{{v_f - v_i}}{{t}}$

Where:

• $a$ is the acceleration,
• $v_f$ is the final velocity,
• $v_i$ is the initial velocity,
• $t$ is the time.

Given:

• Initial velocity $v_i = 40 \, \text{km/h}$,
• Final velocity $v_f = 64 \, \text{km/h}$,
• Time $t = 10 \, \text{seconds}$.

We first calculate the change in velocity:

$\Delta v = v_f - v_i = 64 \, \text{km/h} - 40 \, \text{km/h} = 24 \, \text{km/h}.$

Now, find the acceleration:

$a = \frac{{24 \, \text{km/h}}}{10 \, \text{seconds}} = 2.4 \, \text{km/h per second}.$

To express this as $\text{km/h}^2$, we multiply by 3600 (since 1 second is $\frac{1}{3600}$ hours):

$a = 2.4 \, \text{km/h per second} \times 3600 \, \text{seconds/hour} = 8640 \, \text{km/h}^2.$

But none of the options match this unit form exactly.

So, keeping it in km/h per second terms:

• The correct answer is 2.4 km/h per second.

Would you like to explore more details?

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Here are some related questions to further your understanding:

1. What is the difference between km/h² and km/h per second?
2. How would the calculation change if the time was in minutes?
3. How do you convert between m/s² and km/h²?
4. What is uniform acceleration, and how does it apply here?
5. How does this type of calculation differ for non-linear acceleration?

Tip: Always make sure to convert time units consistently when calculating acceleration!