 A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration?


To find the average acceleration of the roller coaster car, we can use the following formula for average acceleration \( a \):

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

Where:
- \( \Delta v \) is the change in velocity (final velocity - initial velocity)
- \( \Delta t \) is the time interval during which the change occurs.

### Given:
- Initial velocity, \( v_0 = 4 \, \text{m/s} \)
- Final velocity, \( v = 22 \, \text{m/s} \)
- Time interval, \( \Delta t = 3 \, \text{seconds} \)

Now, calculate the change in velocity:
\[
\Delta v = 22 \, \text{m/s} - 4 \, \text{m/s} = 18 \, \text{m/s}
\]

Now, calculate the average acceleration:
\[
a = \frac{18 \, \text{m/s}}{3 \, \text{s}} = 6 \, \text{m/s}^2
\]

### Answer:
The average acceleration of the roller coaster car is \( 6 \, \text{m/s}^2 \).

Would you like more details or explanations on this topic?

Here are 5 related questions for deeper understanding:
1. What is the difference between average acceleration and instantaneous acceleration?
2. How would the acceleration change if the time interval were doubled?
3. What is the significance of negative acceleration, or deceleration?
4. How can we calculate the distance traveled during this time with constant acceleration?
5. Can you explain the relationship between acceleration and force in this scenario?

**Tip:** When acceleration is constant, the change in velocity is linear with time!

A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration?

Learn how to calculate the average acceleration of a roller coaster car, given an initial speed of 4 m/s and a final speed of 22 m/s over a 3-second interval. This problem involves key kinematic concepts, including velocity change and time intervals, suitable for students in Grades 9-11.

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