A jogger accelerates from rest to 3.0 m/s in 2.0 s. A car acceler- ates from 38.0 to 41.0 m/s also in 2.0 s.

(a) Find the acceleration (magnitude only) of the jogger.

(b) Determine the acceleration (magnitude only) of the car.

Let's solve each part of the problem step by step.

### (a) Acceleration of the Jogger

The formula to calculate acceleration is:

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

where:
- \( \Delta v \) is the change in velocity
- \( \Delta t \) is the change in time

For the jogger:
- Initial velocity (\(v_0\)) = 0 m/s (since the jogger starts from rest)
- Final velocity (\(v_f\)) = 3.0 m/s
- Time (\(t\)) = 2.0 s

The change in velocity \( \Delta v \) is:

\[
\Delta v = v_f - v_0 = 3.0 \, \text{m/s} - 0 \, \text{m/s} = 3.0 \, \text{m/s}
\]

Now, calculate the acceleration:

\[
a = \frac{3.0 \, \text{m/s}}{2.0 \, \text{s}} = 1.5 \, \text{m/s}^2
\]

So, the acceleration of the jogger is **1.5 m/s²**.

### (b) Acceleration of the Car

Using the same formula:

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

For the car:
- Initial velocity (\(v_0\)) = 38.0 m/s
- Final velocity (\(v_f\)) = 41.0 m/s
- Time (\(t\)) = 2.0 s

The change in velocity \( \Delta v \) is:

\[
\Delta v = v_f - v_0 = 41.0 \, \text{m/s} - 38.0 \, \text{m/s} = 3.0 \, \text{m/s}
\]

Now, calculate the acceleration:

\[
a = \frac{3.0 \, \text{m/s}}{2.0 \, \text{s}} = 1.5 \, \text{m/s}^2
\]

So, the acceleration of the car is also **1.5 m/s²**.

### Summary
- **Acceleration of the jogger:** 1.5 m/s²
- **Acceleration of the car:** 1.5 m/s²

Would you like more details or have any questions? Here are some related questions for further practice:

1. How would the acceleration change if the jogger reached a speed of 6.0 m/s in the same time?
2. What is the significance of acceleration being the same for both the jogger and the car despite different velocities?
3. If the time for acceleration was reduced to 1 second, how would the acceleration of both the jogger and the car change?
4. Calculate the distance covered by the jogger during the acceleration period.
5. How much kinetic energy did the car gain during its acceleration?

**Tip:** Always keep track of units when calculating physical quantities to ensure accuracy in your results.

Learn how to calculate acceleration using examples of a jogger and a car. Understand the basic physics formula for acceleration, Δv / Δt, and apply it to solve for the magnitude of acceleration in each case. Explore the differences and similarities in acceleration despite different initial and final velocities. Suitable for high school students and physics enthusiasts.

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