Question

A body moves from A to B at a speed of 10 m/s and back to A along the same path at a speed of 20 m/s . Find it's average speed and average velocity for the journey ​

Answer 1

Given :-

▪ A body moves from A to B at a speed of s₁ = 10 m/s and comes back to A along the same path at a speed of s₂ = 20 m/s.

To Find :-

▪ Average speed

▪ Average velocity for the whole journey

Solution :-

The average velocity is 0 m/s. why??

because the body made no displacement at the end of its journey as given in the question that the body comes to the same point i.e., A

Now, Let us find the average speed.

So, we will have to find the total distance travelled and total time.

Let the distance between A and B be d m

So, We have the total distance travelled as 2d (Body comes back to the same point A)

finally, let us find the total time taken,

A to B

we have,

• Distance travelled = d
• Speed, s₁ = 10 m/s

We know,

⇒ Distance = Speed × Time

⇒ t₁ = Distance / Speed

⇒ t₁ = d / 10 ...(1)

B to A

we have,

• Distance travelled = d
• Speed, s₂ = 20 m/s

Similarly,

⇒ Time taken = Distance / Speed

⇒ t₂ = d / 20 ...(2)

Further,

⇒ Total time taken = (1) + (2)

⇒ T = d/10 + d/20

⇒ T = 3d/20 ...(3)

So,

⇒ Average speed = Total distance / Time

⇒ Avg. Speed = 2d / (3d / 20)

⇒ Avg. Speed = 40/3

⇒ Avg. Speed = 13.33 m/s

Hence, The average speed of the whole journey is 13.33 m/s and the average velocity for the whole journey is 0 m/s.

Answer 2

Average speed is the distance traveled divided by the time taken to travel

Each leg of the journey is the same distance, call it d = |AB| (that is just maths-speak for “d is the distance from A to B”).

• We are not told directly what it is… the trick with this sort of question is to just use variables for the things you don’t know and hope it all comes out OK at the end. So keep on going and just put d everywhere we’d normally want to have the actual distance.

• The total distance traveled is 2d because the body does goes over the same ground twice.

• The time on the first leg of the journey is d/10, and for the second part is d/20 (in seconds).

So the total time is d/10 + d/20 = 30d/200

So the average speed is distance over time:

[math]\bar v = \frac{2d}{30d/200} = (40/3)\mathrm{m}\cdot\mathrm{s}^{-1}[/math]

The second part is a trick question, sort of.

The average velocity is the total displacement divided by the total time.

Displacement is a vector … it’s the change in position.

Since the body returns to the same position it started out in, it does not change position overall, so it’s total displacement is zero. Therefore the average velocity is zero.

hope it helps