object a and object b both speed up during a 10 second time interval. object a increases in velocity 10m/s north while object B increases in velocity 5m/s east

In this scenario, both objects A and B experience a change in velocity during the same time interval, but their velocity changes in different directions:

- **Object A** increases its velocity by 10 m/s north.
- **Object B** increases its velocity by 5 m/s east.

### Key Concepts:
1. **Velocity** is a vector, meaning it has both magnitude and direction.
2. The change in velocity (Δv) over time is known as acceleration. Acceleration is also a vector and is calculated by dividing the change in velocity by the time interval.
   
### Let's calculate the acceleration of each object:

- **Object A's acceleration**:
  \[
  a_A = \frac{\Delta v_A}{t} = \frac{10 \, \text{m/s}}{10 \, \text{s}} = 1 \, \text{m/s}^2 \, \text{north}
  \]

- **Object B's acceleration**:
  \[
  a_B = \frac{\Delta v_B}{t} = \frac{5 \, \text{m/s}}{10 \, \text{s}} = 0.5 \, \text{m/s}^2 \, \text{east}
  \]

These accelerations are in different directions, so they cannot be directly compared without using vector addition. If we wanted to calculate the resultant acceleration of both objects combined (assuming we treat them as a single system), we would add these vectors.

### Resultant acceleration:
The magnitude of the resultant acceleration \(a_{\text{resultant}}\) can be found using the Pythagorean theorem since the accelerations are perpendicular (north and east).

\[
a_{\text{resultant}} = \sqrt{(a_A)^2 + (a_B)^2} = \sqrt{(1^2 + 0.5^2)} = \sqrt{1 + 0.25} = \sqrt{1.25} \approx 1.12 \, \text{m/s}^2
\]

The direction of the resultant acceleration can be found using trigonometry (tan inverse of the ratio of the accelerations).

Do you want to see details of how to find the direction, or any clarifications?

### Related Questions:
1. What is the difference between speed and velocity?
2. How do you add vector quantities in physics?
3. How does acceleration relate to Newton's second law of motion?
4. Can an object have zero velocity and still be accelerating?
5. How would the analysis change if the two accelerations were in the same direction?

### Tip:
Always remember that velocity and acceleration are vector quantities, which means they must include both magnitude and direction for complete description.

Learn how to calculate the acceleration of two objects moving in different directions over a 10-second interval. Object A moves north with a velocity increase of 10 m/s, and object B moves east with a velocity increase of 5 m/s. Includes vector addition and the Pythagorean theorem to find the resultant acceleration.

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