Question

John drove south 12 km at 4 km per hour and then East 15 km at 3 km per hour. Determine the average speed and average velocity of whole journey

Answer 1

Explanation:

As per the provided information in the given question, we have :

• John drove south 12 km at 4 km/h and then East 15 km at 3 km/h.

We've been asked to calculate average speed and average velocity.

Let us suppose that John travels 12 km due south from A to B and the he travels 15 km due east from B to C.

In order to calculate the average speed of John, firstly we need to calculate total distance travelled and total time taken.

↠Total distance = 12 km + 15 km

↠Total distance = 27 km

Now, we need to calculate total time. Total time would be the sum of time taken to cover the distance from A to B and time taken to cover the distance from B to C.

↠Total time = t₁ + t₂

• t₁ = Time taken to cover the distance from A to B
• t₂ = Time taken to cover the distance from B to C.

• Time = Distance ÷ Speed

↠Total time = {¹²/₄ + ¹⁵/₃} hr

↠Total time = {3 + 5} hr

↠Total time = 8 hours

Now, as it is know to us that,

$\\ \longrightarrow \quad \boxed{\pmb{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }} }$

Substitute the values.

↠Average Speed = ²⁷/₈ km/h

↠Average Speed = 3.375 km/h

∴ The average speed of John is 3.375 km/h.

⠀⠀⠀⠀⠀_____________

We've to find the average velocity also, for that we need to calculate total displacement and total time. We've already calculated the total time , that is 8 hours. Here, the total displacement is AC which is the shortest distance from his initial to final position.

↠Total displacement = √(AB² + BC²)

↠Total displacement = √{ (12)² + (15)² }

↠Total displacement = √(144 + 225)

↠Total displacement = √369

↠Total displacement = 19.20 km towards south east

Now, as we know that,

$\\ \longrightarrow \quad \boxed{\pmb{\sf {Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time} }} }$

↠ Average velocity = 19.20 km towards south east ÷ 8 h

↠ Average velocity = 2.4 km towards south east

∴ The average speed of John is 3.375 km/h and the average velocity of John is 2.4 km/h towards south east.

Answer 2

Answer:

please refer the attachment...