[b][color=#cc0000]Particle A [/color][/b]starts at the point (50, 0) and [color=#cc0000][b]heads west as a speed of 10 m/s[/b][/color]. [br][b][color=#0000ff]Particle B[/color][/b] starts at the point (0, 40) and [color=#0000ff][b]heads south at a speed of 5 m/s[/b][/color]. [br][br]Play to animate, then answer the questions that follow.
Determine the rate at which [i]p, [/i]the distance between [i]A[/i] and [i]B[/i], is changing with respect to time at [i]t[/i] = 2 sec.
You can check your answer in the applet.
Explain why, with respect to the physical context here, [math]\frac{dp}{dt}<0[/math] at [i]t[/i] = 2 sec.
Since the distance [i]p[/i] between [i]A[/i] and [i]B[/i] is decreasing at time [i]t = [/i]2 sec, [math]\frac{dp}{dt}<0[/math] here. Remember, if a function is decreasing at a certain input value, this function's derivative will be negative when evaluated at that input value.
At what time is [math]\frac{dp}{.dt}=0[/math]? (You can informally verify by interacting with the applet, but be sure to formally show this using calculus!)