Average and Instantaneous Velocity

What is the difference between average velocity and average speed?

Explain why average velocity is a vector quantity.

Calculate the average velocity of a particle that undergoes a displacement of (10 m)𝑗̂ in 5 seconds.

If a particle's displacement vector is (5 m)𝑖̂ + (12 m)𝑗̂ and it takes 4 seconds, what is its average velocity?

What mathematical expression defines average velocity?

If the total distance covered is 30 m in 5 seconds, what is the average speed?

Why is average speed considered a scalar quantity?

What is the significance of the direction associated with average velocity?

Given the average velocity of (6 m/s)𝑖̂ + (1.5 m/s)𝑘̂ over 2 seconds, what is the corresponding displacement?

Describe how you would determine average velocity in a multi-dimensional motion.

Defined as the rate of change of position over a specific time interval.
Calculated as the ratio of overall displacement to the corresponding time interval:
- ( v_{\text{avg}} = \frac{\Delta r}{\Delta t} ).
Given by the equation:
- ( v_{\text{avg}} = \frac{r_2 - r_1}{t_2 - t_1} ).
Average velocity is a vector quantity, involving both magnitude and direction.
Direction of average velocity aligns with the displacement vector ( \Delta r ).

Represents how fast an object travels over a distance in a designated time interval.
Calculated as the total distance traveled divided by the total time taken:
- ( s_{\text{avg}} = \frac{\text{total distance}}{\text{total time}} ).
Average speed is a scalar quantity, indicating no direction.
Magnitude of average speed equals the magnitude of average velocity:
- ( |s_{\text{avg}}| = |v_{\text{avg}}| ).

For a particle with displacement ( \Delta r = (12 , \text{m})\hat{i} + (3.0 , \text{m})\hat{k} ) in 2.0 seconds:
- Average velocity calculation yields:
  - ( v_{\text{avg}} = \frac{(12 , \text{m})\hat{i} + (3.0 , \text{m})\hat{k}}{2.0 , \text{s}} = (6.0 , \text{m/s})\hat{i} + (1.5 , \text{m/s})\hat{k} ).