Velocity and Acceleration of a particle

Click For Summary
SUMMARY

The discussion focuses on determining the position, velocity, and acceleration of a particle described by the parametric equations x(t) = (1.5 m/s)t + (-0.5 m/s²)t² and y(t) = 6 m + (-3 m/s)t + (1.5 m/s²)t². The velocity components v(x) and v(y) are derived by differentiating the position functions with respect to time. To find the time(s) when the horizontal and vertical components of velocity are equal, set v(x) equal to v(y) and solve for t. Additionally, to find when the particle's x and y coordinates are equal, set x(t) equal to y(t) and solve for t.

PREREQUISITES
  • Understanding of calculus, specifically differentiation
  • Familiarity with parametric equations
  • Knowledge of kinematic equations in physics
  • Ability to solve algebraic equations
NEXT STEPS
  • Study the process of differentiation in calculus
  • Learn about parametric equations and their applications
  • Explore kinematic equations for motion analysis
  • Practice solving systems of equations for multiple variables
USEFUL FOR

Students studying physics or calculus, educators teaching motion concepts, and anyone interested in the mathematical analysis of particle dynamics.

cougar_21
Messages
15
Reaction score
0
Velocity and Acceleration Please Help!

My problem reads:

A particle is observed to move with the coordinates x(t)=(1.5m/s)t + (-0.5 m/s^2)t^2 and y(t) = 6m + (-3m/s)t + (1.5 m/s^2)t^2. What are the particle's position, velocity, and acceleration? At what time(s) are the velocity's horizontal and vertical components equal?

I got the derivative of x(t) and y(t) to get v(x) and v(y). Where do I go from there :confused:
 
Physics news on Phys.org
do get the acceleration take the derivative of V(x) and V(y).

For the what time thing, set them equal, solve for "t"?
 
For the second question, solve for x(t) = y(t).
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 38 ·
2
Replies
38
Views
5K
  • · Replies 5 ·
Replies
5
Views
4K
Replies
2
Views
1K
Replies
12
Views
2K
Replies
11
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K