Velocity vector and velocity intensity

In summary, to find the average velocity vector and velocity intensity over a time period of [0, π/2w], the formula for average velocity is used, which results in an average velocity of aw. For the velocity intensity, the formula v = √(v^2r + v^2θ) is used, which simplifies to v = aw. Therefore, the velocity intensity is also aw.
  • #1
doktorwho
181
6

Homework Statement


Given the velocity vector in the polar coordinates, ##\vec v=-awsin{wt}\vec e_r + awcos{wt}\vec e_\theta## determine the average velocity vector and velocity intensity over a time period ##[0, \pi/2w]##

Homework Equations


3. The Attempt at a Solution [/B]
For the first part where the average velocity vector is to be found i use
##\vec v_{avg}=\frac{\int_{0}^{\pi/2w}\vec vdt}{\pi/2w}##
and for the intensity part i use
##v=\sqrt{v^2_r+v^2_\theta}## first find the intensity which is just ##v=aw## and since the intensity is equal at all times i get for the second part
##\frac{2aw}{\pi/2w}## but i don't get correct results, where is my mistake?
 
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  • #2
doktorwho said:
For the first part where the average velocity vector is to be found i use
##\vec v_{avg}=\frac{\int_{0}^{\pi/2w}\vec vdt}{\pi/2w}##
Which resulted in ...?
doktorwho said:
and for the intensity part i use
##v=\sqrt{v^2_r+v^2_\theta}## first find the intensity which is just ##v=aw## and since the intensity is equal at all times
right.
doktorwho said:
i get for the second part
##\frac{2aw}{\pi/2w}##
Think again about that step.
 
  • #3
haruspex said:
Which resulted in ...?

right.

Think again about that step.
Well.. isn't average acceleration then just ##(v_i+v_f)/2##? Shouldnt i just get ##aw## then?
 
  • #4
doktorwho said:
Well.. isn't average acceleration then just ##(v_i+v_f)/2##? Shouldnt i just get ##aw## then?
Yes. No need to divide by the period.
 
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Related to Velocity vector and velocity intensity

What is a velocity vector?

A velocity vector is a mathematical representation of an object's motion, including both its speed and direction. It is typically represented as an arrow, with the length representing the speed and the direction of the arrow representing the direction of motion.

How is velocity vector different from speed?

Velocity vector includes both speed and direction, whereas speed only refers to the rate of change of an object's position. Velocity vector is a vector quantity, while speed is a scalar quantity.

What is the formula for calculating velocity vector?

The formula for velocity vector is: velocity = displacement / time. This means that the velocity vector is equal to the change in an object's position divided by the time it takes to make that change.

What is velocity intensity?

Velocity intensity refers to the magnitude or strength of an object's velocity vector. It is the numerical value of the velocity, without taking into account the direction of the motion.

How is velocity intensity related to acceleration?

Velocity intensity and acceleration are related because acceleration is the rate of change of velocity. This means that a change in velocity intensity can indicate the presence of acceleration, either in the form of speeding up or slowing down.

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