To calculate the acceleration of the car, we need to understand the change in velocity over time. Here’s how we can do it:

Given:

• Initial velocity ($v_i$): 40 km/h
• Final velocity ($v_f$): 64 km/h
• Time interval ($\Delta t$): 10 seconds

Step 1: Convert velocities from km/h to m/s

We convert km/h to m/s using the conversion factor $\frac{5}{18}$:

$v_i = 40 \times \frac{5}{18} = \frac{200}{18} \approx 11.11 \text{ m/s}$

$v_f = 64 \times \frac{5}{18} = \frac{320}{18} \approx 17.78 \text{ m/s}$

Step 2: Calculate the change in velocity ($\Delta v$)

$\Delta v = v_f - v_i = 17.78 \text{ m/s} - 11.11 \text{ m/s} = 6.67 \text{ m/s}$

Step 3: Calculate the acceleration ($a$)

The acceleration $a$ is given by the formula:

$a = \frac{\Delta v}{\Delta t}$

Substituting the values:

$a = \frac{6.67 \text{ m/s}}{10 \text{ s}} = 0.667 \text{ m/s}^2$

Final Answer:

The acceleration of the car is approximately $0.667 \text{ m/s}^2$.

Would you like further details or have any other questions?

Here are 5 related questions:

1. How would the acceleration change if the time was 5 seconds instead of 10?
2. What is the significance of negative acceleration, or deceleration?
3. How do you find the distance traveled during this acceleration?
4. What would the final velocity be after 15 seconds of acceleration at this rate?
5. Can you calculate acceleration if only distance and time are given?

Tip: Always double-check unit conversions, especially when working with time and speed in different units.