Distance from Origin to Moving Point: y=x^2+1, dx/dt=2cm/s

  • Thread starter Thread starter mattsoto
  • Start date Start date
  • Tags Tags
    Origin Point
Click For Summary
SUMMARY

The discussion focuses on calculating the rate of change of the distance between the origin and a moving point on the curve defined by the equation y = x² + 1, given that dx/dt = 2 cm/s. The distance formula from the origin to a point (x, y) is derived as d = √(x² + y²), which simplifies to d² = x² + (x² + 1)². By applying implicit differentiation and substituting dx/dt, participants can find the rate of change of distance with respect to time.

PREREQUISITES
  • Understanding of calculus, specifically differentiation
  • Familiarity with the distance formula in a Cartesian coordinate system
  • Knowledge of implicit differentiation techniques
  • Basic understanding of the function y = x² + 1
NEXT STEPS
  • Study implicit differentiation in calculus
  • Learn how to apply the distance formula in two dimensions
  • Explore related rates problems in calculus
  • Investigate the geometric interpretation of derivatives
USEFUL FOR

Students studying calculus, educators teaching related rates, and anyone interested in applying mathematical concepts to real-world motion problems.

mattsoto
Messages
5
Reaction score
0
"Find the rate of chage of the distance between the origin and the moving point on the graph of y=x^2+1 if dx/dt=2 centimeters per second."...im sure it is a simple problem...any help?
 
Physics news on Phys.org
You'll get more response if you describe what you've tried or what you are thinking.
 
What IS the distance between the origin and any point (x,y)?

What is the distance if the point lies on the curve y= x2+ 1?

Hint: In problems with distances, it is often simpler to work with "distance2" than with distance itself!
 

Similar threads

A point moves along the curve y=2x^2+1
  • · Replies 2 ·
Replies
2
Views
14K
Determine whether ## S[y] ## has a maximum or a minimum
  • · Replies 18 ·
Replies
18
Views
4K
A line integral about a closed "unit triangle" around the origin
  • · Replies 12 ·
Replies
12
Views
5K
Polar equation of a hyperbola with one focus at the origin
  • · Replies 6 ·
Replies
6
Views
2K
How should I find ## x_{2}(t) ## for this nonlinear integro-differential equation?
  • · Replies 6 ·
Replies
6
Views
3K
Find f'(x): f'(x) = ##\frac {dy} {dx},\frac {dx}{dt}= \frac {8t^7}{1+t^{16}} ##
  • · Replies 48 ·
2
Replies
48
Views
4K
How Do You Solve the Differential Equation dy/dx = 1 - y^2?
  • · Replies 12 ·
Replies
12
Views
3K
Finding the distance from origin to a tangent line
  • · Replies 15 ·
Replies
15
Views
5K
Volume integral of x^2 + (y-2)^2 +z^2 = 4 where x , y , z > 0
  • · Replies 21 ·
Replies
21
Views
3K
Moving point and it's distance relative to a fixed point
  • · Replies 2 ·
Replies
2
Views
2K