Help with Vectors: Finding Average Velocity

  • Thread starter Thread starter coopvtcc
  • Start date Start date
  • Tags Tags
    Vectors
Click For Summary
SUMMARY

The discussion focuses on calculating the average velocity of a dot in an animation, defined by the position vector r = [3.5 cm + (2.8 cm/s²)t²]i + (5.4 cm/s)t.j. To find the average velocity between t = 0 and t = 2.2 s, users are instructed to substitute the time values into the position equation and apply the distance/time formula. The magnitude is determined using Pythagoras' theorem, while the direction is calculated using the arctan function based on the x and y components derived from the vector.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with Pythagorean theorem
  • Knowledge of trigonometric functions, specifically arctan
  • Basic principles of kinematics
NEXT STEPS
  • Study vector calculus for deeper insights into motion analysis
  • Learn about kinematic equations in physics
  • Explore the use of animation tools for visualizing motion
  • Investigate advanced topics in physics such as projectile motion
USEFUL FOR

Students in physics or engineering, web developers creating animations, and anyone interested in understanding motion dynamics through vector analysis.

coopvtcc
Messages
1
Reaction score
0
A web page designer creates an animation in which a dot on a computer screen has a position of r= [3.5 cm + (2.8 cm/s2)t2]i + (5.4 cm/s)t.j

(a) Find the magnitude and direction of the dot's average velocity between t = 0 and t = 2.2 s
 
Physics news on Phys.org
coopvtcc said:
A web page designer creates an animation in which a dot on a computer screen has a position of r= [3.5 cm + (2.8 cm/s2)t2]i + (5.4 cm/s)t.j

(a) Find the magnitude and direction of the dot's average velocity between t = 0 and t = 2.2 s

the operations/operands being multiplied to i and j are just scalars (regular numbers), you can just plug in the values of t and use the distance/time formula. Then the direction of the final vector may be determined by an angle off the horizon. If you have your vector coming from the origin (0,0), you will know the length of your sides, then you can just take arctan( ratio of sides ). For magnitude, use pygthoras' theorem for the x side and the y side you can imagine from your x and y components
 

Similar threads

Two Equations for Average Velocity?
  • · Replies 2 ·
Replies
2
Views
3K
How do I derive an expression for the velocity vector for any α?
  • · Replies 26 ·
Replies
26
Views
4K
Solving Vector Diagrams: Finding Displacements & Velocities
  • · Replies 5 ·
Replies
5
Views
2K
Calculate Distance Traveled: Instantaneous vs. Average Velocity
  • · Replies 5 ·
Replies
5
Views
2K
Are the 2nd and 3rd problems in this video correctly solved? (charged dipole and organ pipe problems)
  • · Replies 3 ·
Replies
3
Views
1K
Find the height of a lamp based on the velocities of projectiles
  • · Replies 40 ·
2
Replies
40
Views
3K
What is the displacement and average velocity of a classic car in a road rally?
  • · Replies 1 ·
Replies
1
Views
2K
Vectors, how to find average acceleration
  • · Replies 13 ·
Replies
13
Views
7K
How Do You Calculate Instantaneous Velocity in Vector Animation?
  • · Replies 2 ·
Replies
2
Views
19K
2-D Kinematic Velocity and Acceleration Practice Problem
  • · Replies 2 ·
Replies
2
Views
2K