# The change in velocity betwen two points

• Sleve123
In summary, the conversation is about calculating the speed, average velocity, and change in velocity of a particle traveling on a semi-circular path from point A to B. The diameter of the path is 200m and it takes 80 seconds to travel. The agreed upon answers for a) and b) are 3.93 m/s and 2.5 m/s in the direction of A to B, respectively. However, there is a disagreement about the change in velocity, with the lecturer calculating 5 m/s and the individual calculating 7.85 m/s. The individual explains their reasoning using a vector approach and the orientation of the semicircle in relation to the coordinate system. They also mention being on a teacher training
Sleve123
Here's a question that I got in my mechanics tutorial.

--------------------------------------------------------------------

A particle travels on a semi-circular path from A to B -

The diameter being 200m, the time taken 80 seconds, Calculate:

a) its speed

b) average velocity from A to B

c) the change velocity from A to B

----------------------------------------------------------------------

Me and my lecturer agree that a) is 3.93 m/s, b) is 2.5 m/s (in the direction A to B), but we disagree on c).

My lecturer got 5 m/s and me 7.85 m/s, are we both wrong or are one of us right?

Also it would be helpful to expalin how you get to the answer (if I'm wrong).

Sleve123 said:
Here's a question that I got in my mechanics tutorial.

--------------------------------------------------------------------

A particle travels on a semi-circular path from A to B -

The diameter being 200m, the time taken 80 seconds, Calculate:

a) its speed

b) average velocity from A to B

c) the change velocity from A to B

----------------------------------------------------------------------

Me and my lecturer agree that a) is 3.93 m/s, b) is 2.5 m/s (in the direction A to B), but we disagree on c).

My lecturer got 5 m/s and me 7.85 m/s, are we both wrong or are one of us right?

Also it would be helpful to expalin how you get to the answer (if I'm wrong).

Can you explain your answer to c? And what is the direction of the change in velocity that you list?

berkeman said:
Can you explain your answer to c? And what is the direction of the change in velocity that you list?

I worked it out like this:

I'm assuming that the velocity is always at a tangent to the circle (in this case a semi circle),
then the velocity at A and B, will be of the same magnitude (the speed 3.926 m/s) but in opposite directions, therefore the difference will be:

Change in velocity (from A to B) = Velocity at A - Velocity at B

but Velocity at B = - Velocity at A because they are opposite directions, therefore--->

Change in velocity (from A to B) = Velocity at A - - Velocity at A = 2 x (Velocity at A)

= 2 x 3.926 = 7.85 m/s

Last edited:
Sleve123 said:
I worked it out like this:

I'm assuming that the velocity is always at a tangent to the cricle (in this case a semi cirle),
then the velocity at A and B, will be of the same magnitude (the speed 3.926 m/s) but in opposite directions, therefore the difference will be:

Change in velocity (from A to B) = Velocity at A - Velocity at B

but Velocity at B = - Velocity at A because they are opposite directions, therefore--->

Change in velocity (from A to B) = Velocity at A - - Velocity at A = 2 x (Velocity at A)

= 2 x 3.926 = 7.85 m/s

That was my thought as well. However, you need to define a coordinate system in order to get the sign correct. Velocity is a vector quantity, with magnitude and direction. So the direction of the vectors in the coordinate system makes a difference.

berkeman said:
That was my thought as well. However, you need to define a coordinate system in order to get the sign correct. Velocity is a vector quantity, with magnitude and direction. So the direction of the vectors in the coordinate system makes a difference.

Thanks - Yeah I've worked it out using vectors (gives the same answer), but you can see from a diagram that there is no horizontal components of velocity so I didn't bother in my working above.

I tried to explain this to him but he was having none of it, I'm on a teacher training course (I did an engineering degree and I am converting) but many on the course haven't done much maths, so I thought I was going nuts.

Sleve123 said:
Thanks - Yeah I've worked it out using vectors (gives the same answer), but you can see from a diagram that there is no horizontal components of velocity so I didn't bother in my working above.

I tried to explain this to him but he was having none of it, I'm on a teacher training course (I did an engineering degree and I am converting) but many on the course haven't done much maths, so I thought I was going nuts.

The orientation of the semicircle to the coordinate system does matter. If the coordinate system is x to the right and y pointing up to the top of the page, and the semicircle is drawn on the top half of the coordinate system, then the initial velocity is in the +y direction, and the final is in the -y direction, so the magnitude of the change is twice the initial magnitude, but the sign is negative (since it started positive, and ends negative).

berkeman said:
The orientation of the semicircle to the coordinate system does matter. If the coordinate system is x to the right and y pointing up to the top of the page, and the semicircle is drawn on the top half of the coordinate system, then the initial velocity is in the +y direction, and the final is in the -y direction, so the magnitude of the change is twice the initial magnitude, but the sign is negative (since it started positive, and ends negative).

Thanks, I get it all now.

## 1. What is velocity?

Velocity is a vector quantity that describes the rate of change of an object's position. It includes both the speed and direction of an object's motion.

## 2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position by the change in time. This can be represented by the equation: velocity = (change in position) / (change in time).

## 3. What is the difference between velocity and speed?

While both velocity and speed describe how fast an object is moving, velocity also includes the direction of motion. Speed is a scalar quantity, meaning it only has magnitude, while velocity is a vector quantity with both magnitude and direction.

## 4. What is the change in velocity between two points?

The change in velocity between two points is the difference in an object's velocity at those two points. This can be calculated by subtracting the initial velocity from the final velocity.

## 5. What factors can cause a change in velocity between two points?

The change in velocity between two points can be caused by a change in speed, direction, or both. This can be a result of forces acting on the object, such as acceleration, or a change in the environment, such as a change in air resistance.

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