SOLUTION: A particle travels along the parabola y = 5x^2 + x + 3. At what point do its abscissa and ordinate change at the same rate.

Question 1082943: A particle travels along the parabola y = 5x^2 + x + 3. At what point do its abscissa and ordinate change at the same rate.

Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!



The abscissa and ordinate change at the same rate when 



Differentiate 



with respect to t (use the chain rule) 



Since , we divide equals by equals by dividing
the left side by  and the right side through by 







So the abscissa and ordinate change at the same rate when x=0,
and that is when  





So the abscissa and ordinate change at the same rate at the
point (0,3)

Edwin

RELATED QUESTIONS
a point moves on the parabola y^2=16x in such a way that the rate of change of the... (answered by ikleyn)

A particle is moving in the positive direction, away from the origin along the graph of y (answered by ikleyn)

A particle is moving along the curve y= 3 \sqrt{5 x + 6}. As the particle passes through... (answered by Fombitz)

A point moves on the parabola y^2 = 8 in such a way that the rate of change of the... (answered by Alan3354)

A particle is moving along the curve y= 3√4x+4. As the particle passes through the... (answered by Alan3354)

The point P(x, y) lies on the parabola y=(1/2)x^2. Find this point such that the sum S of (answered by stanbon,ikleyn)

The graph of a linear function intersects with the x axis at a point with an abscissa of... (answered by Alan3354)

A bug is moving along the right side of the parabola y = x^2 at a rate such that its... (answered by Fombitz)

a line of slope 3 passes through the point (7,10). if a point on the line has an abscissa (answered by josgarithmetic)