Find distance, velocity vectors

[kbowman]

Hi there, I really need help with this one part of an assignment! We never covered this in my lectures, however I have an assignment due on this.. which is not impressing me.
Even if you should tell me step by step on how I could answer this, or show me via examples used in the problem, I would be forever grateful!
Thankyou for all your help,
Kat

 

[andrevdh]

Ex. 2
(a) Have a go at this and we will help you to do it. Show your attempt at this part of the problem in a post here.
(b) This part requires you to use the relationship between an angular measure in a different unit, radians, not degrees. Let's say the angle is at a point A. The two arms of the angle extend outwards. You are required to determine the angle in radians of this angle. First you draw a circle with point A as the centre through the two arms. The radius of the circle is r. The circle cut the two arms at the points B and C. You need to determine the distance s along the circle between the two points B and C. The angle in radians is then given by

$$\theta _r = \frac{s}{r}$$

This angular measure have no dimension as you see. For an angle of $360^o$ it comes to $2\pi$ radians (see if you can get this yourself).

To solve this part convert the given angle to radians and then calculate the arc distance with the known radius.

To convert from degrees to radians note that you need to calculate the angle in degrees by a conversion factor of ''units" [radians per degree]. From the example above this conversion factor will come to

$$\frac{2\pi}{360^o}$$

 

[kyle8921]

Hi Kat,

I understand that you are struggling with finding distance and velocity vectors for an assignment. I am happy to help you with this concept.

To start, distance is the total length traveled by an object in a given time period. It is a scalar quantity, meaning it only has a magnitude and no direction. Velocity, on the other hand, is a vector quantity that describes the rate of change of an object's position. It includes both magnitude (speed) and direction.

To find the distance traveled by an object, you can use the formula d = vt, where d is the distance, v is the velocity, and t is the time. This formula assumes that the velocity is constant throughout the entire time period.

For example, if an object travels at a constant velocity of 10 m/s for 5 seconds, the distance traveled would be 50 meters (d = 10 m/s x 5 s).

Now, to find the velocity vector, you need to know the direction of the object's motion. This can be represented by an arrow pointing in the direction of motion. The length of the arrow represents the speed or magnitude of the velocity.

For instance, if an object is moving at a velocity of 10 m/s to the right, the velocity vector would be represented by an arrow pointing to the right with a length of 10 units.

I hope this helps you understand how to find distance and velocity vectors. If you have any further questions or need more examples, please do not hesitate to ask. Good luck with your assignment!

Best,