a car increases its speed at constant rate from 64 kph at A to 96 kph at 8. what is the magnitude of its acceleration 2 sec after the car passes point A? (14.3 m/s^2)

To find the magnitude of the car's acceleration \( 2 \) seconds after passing point \( A \), we can use the following steps.

### Step 1: Convert the speeds from kph to m/s
First, let's convert the initial speed \( v_A = 64 \) kph and the final speed \( v_B = 96 \) kph into meters per second (m/s).

\[
v_A = 64 \times \frac{1000}{3600} = 17.78 \text{ m/s}
\]
\[
v_B = 96 \times \frac{1000}{3600} = 26.67 \text{ m/s}
\]

### Step 2: Determine the rate of acceleration
Since the acceleration is constant, we can use the formula:

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

Here, \( \Delta v = v_B - v_A \), and \( \Delta t = 8 \) seconds, which gives:

\[
\Delta v = 26.67 \, \text{m/s} - 17.78 \, \text{m/s} = 8.89 \, \text{m/s}
\]

\[
a = \frac{8.89 \, \text{m/s}}{8 \, \text{s}} = 1.11 \, \text{m/s}^2
\]

### Step 3: Find the speed after 2 seconds
The speed after 2 seconds, \( v_2 \), can be found using the equation:

\[
v_2 = v_A + a \times t
\]

Here, \( t = 2 \) seconds:

\[
v_2 = 17.78 \, \text{m/s} + 1.11 \, \text{m/s}^2 \times 2 \, \text{s} = 19.00 \, \text{m/s}
\]

### Step 4: Calculate the acceleration 2 seconds after point \( A \)
The magnitude of the acceleration at 2 seconds is still the constant acceleration we calculated:

\[
a = 1.11 \, \text{m/s}^2
\]

However, it seems you mentioned \( 14.3 \, \text{m/s}^2 \) in your question. This value doesn't match the result from the calculations. If there was a different interpretation or additional information regarding this problem, please clarify.

Would you like to go through the details or have any questions?

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**Related Questions:**

1. How would the problem change if the car's acceleration was not constant?
2. What is the distance traveled by the car in the first 2 seconds?
3. How would the acceleration change if the car reached \( 120 \) kph in \( 10 \) seconds?
4. How does the unit conversion from kph to m/s impact the accuracy of the calculations?
5. How would the scenario change if the car started from rest?

**Tip:** Always ensure you understand whether the problem assumes constant or variable acceleration, as this greatly influences the approach to solving it.

Learn how to calculate the acceleration and speed of a car that increases from 64 kph to 96 kph in 8 seconds with constant acceleration. Detailed step-by-step solution included.

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