6. describe an example (with numerical values) where an object has an average velocity is zero but the…

Explanation:

Step1: Recall definitions

Average velocity is displacement over time, average speed is distance over time. Displacement is zero when object returns to start.

Step2: Construct example

Let’s take a car. It travels 100 km east at 100 km/h (time ( t_1 = \frac{100\ \text{km}}{100\ \text{km/h}} = 1\ \text{h} )), then 100 km west at 100 km/h (time ( t_2 = \frac{100\ \text{km}}{100\ \text{km/h}} = 1\ \text{h} )).

Step3: Calculate displacement and distance

Total displacement: ( 100 - 100 = 0\ \text{km} ). Total distance: ( 100 + 100 = 200\ \text{km} ). Total time: ( 1 + 1 = 2\ \text{h} ).

Step4: Calculate velocity and speed

Average velocity: ( \frac{0\ \text{km}}{2\ \text{h}} = 0\ \text{km/h} ). Average speed: ( \frac{200\ \text{km}}{2\ \text{h}} = 100\ \text{km/h} ).

Answer:

Consider a car that travels 100 km east at a speed of 100 km/h (taking 1 hour) and then travels 100 km west at a speed of 100 km/h (taking another 1 hour). The total displacement of the car is ( 100\ \text{km} - 100\ \text{km} = 0\ \text{km} ), so the average velocity (displacement divided by total time) is ( \frac{0\ \text{km}}{1\ \text{h}+1\ \text{h}} = 0\ \text{km/h} ). The total distance traveled is ( 100\ \text{km} + 100\ \text{km} = 200\ \text{km} ), and the total time is ( 2\ \text{h} ), so the average speed (distance divided by total time) is ( \frac{200\ \text{km}}{2\ \text{h}} = 100\ \text{km/h} ).