A car is traveling down a road at 40 km/h. After 10 seconds, the car is traveling at 64 km/h.

What is the acceleration of the car?

Responses




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

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

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

### Given:
- Initial velocity (\( v_i \)) = 40 km/h
- Final velocity (\( v_f \)) = 64 km/h
- Time (\( \Delta t \)) = 10 seconds

### Step 1: Convert velocities from km/h to m/s
1 km/h is equivalent to \(\frac{5}{18}\) m/s. So,

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

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

### Step 2: Calculate the change in velocity
\[
\Delta v = v_f - v_i = 17.78 - 11.11 = 6.67 \text{ m/s}
\]

### Step 3: Calculate the acceleration
\[
a = \frac{6.67 \text{ m/s}}{10 \text{ s}} = 0.667 \text{ m/s}^2
\]

### Final Answer:
The acceleration of the car is approximately \( 0.667 \text{ m/s}^2 \).

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you convert between different units of speed?
2. What would the acceleration be if the car reached 80 km/h instead?
3. How can you graphically represent this acceleration?
4. How do you calculate deceleration if the car slows down?
5. What is the difference between uniform and non-uniform acceleration?

**Tip:** Always ensure units are consistent when performing calculations, especially when dealing with velocity and acceleration.

Discover how to calculate the acceleration of a car moving from 40 km/h to 64 km/h over a duration of 10 seconds. Follow a detailed step-by-step solution using the acceleration formula. Suitable for students and enthusiasts interested in physics and motion mechanics.

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