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

2.4 km/h2
2.4 km/h squared

4.0 km/h2
4.0 km/h squared

6.4 km/h2
6.4 km/h squared

10.4 km/h2

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?

---

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!

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?

Find the acceleration of a car that increases its speed from 40 km/h to 64 km/h in 10 seconds. This problem uses the acceleration formula a = (v_f - v_i) / t and covers key kinematic concepts. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation