Question

A particle moves along the curve for . The -coordinate of the particle changes at a constant rate of units per second. At the instant when the -coordinate of the particle is , what is the rate of change of the -coordinate of the particle, in units per second?

Answer 1

The rate of change of the y-coordinate cannot be determined without the equation for the y-coordinate.

Step-by-step explanation:

To find the rate of change of the y-coordinate of the particle, we need to differentiate the equation for the y-coordinate with respect to time. However, the equation for the y-coordinate of the particle is not given in the question.

Therefore, we cannot determine the rate of change of the y-coordinate of the particle without the equation for the y-coordinate. Please provide the equation for the y-coordinate of the particle to proceed with finding its rate of change.

Answer 2

To find the rate of change of the y-coordinate of the particle, we need to differentiate the equation for the y-coordinate with respect to time. The rate of change will be constant since the y-coordinate is changing at a constant rate. However, we need to know the value of the y-coordinate at a specific instant to determine the rate of change.

Step-by-step explanation:

In order to find the rate of change of the y-coordinate of the particle, we need to differentiate the equation for the y-coordinate with respect to time. Since the y-coordinate is changing at a constant rate of units per second, the derivative with respect to time will be constant. Let's denote the y-coordinate as y(t). Therefore, we have:

dy/dt = units per second

Now let's substitute the given information into this equation. At the instant when the x-coordinate of the particle is , the y-coordinate is not given. We need to know the value of y(t) in order to determine the rate of change of the y-coordinate. Can you please provide the value of the y-coordinate at that instant?