I'm having difficulty with this problem, and really, I have no idea where to start, where to go, or where to end. I just started a Calculus class a few weeks ago, and i'm learning the basics, but haven't quite mastered application. I'm trying to add a PDF but it says file is too big, so.. Not really sure what to do about that. Anyway, I guess I'll write the problem word for word.
The position P(t) of an object moving along a line is given by the graph below. Where P(t) is in meters and t represents time, in seconds. Be sure to use units in your answers whenever appropriate.
a. Explain what P(0) and P(3) signify. What sense might you make of P(-1)?
My guess: Truly I don't get it. At P(0) no time has lapsed but the object is at 2 meters? And P(3) the object begins to move very rapidly? P(-1) the object is moving very rapidly however it's in negative time? Or behind the accepted starting position?
b. Find the average velocity of the object between 1 seconds and 4 seconds. Is this exact or approximate?
My guess: Uhm, well at 4 seconds the object appears to be moving at a rate of 5 meters per second, and if I had a function I would find the limit to prove this, but how can I do that without a function? At 1 second the object is moving at -0.7 meters per second? A.k.a going backwards? So the average speed would be 1.65 meters per second? I would say this is approximate.
c. For what times t is the object's velocity positive? For what times is the velocity negative?
My guess: Does this mean the intervals where the graph has a negative slope versus a positive slope? Or where the graph is above/below x=0?
The position P(t) of an object moving along a line is given by the graph below. Where P(t) is in meters and t represents time, in seconds. Be sure to use units in your answers whenever appropriate.
a. Explain what P(0) and P(3) signify. What sense might you make of P(-1)?
My guess: Truly I don't get it. At P(0) no time has lapsed but the object is at 2 meters? And P(3) the object begins to move very rapidly? P(-1) the object is moving very rapidly however it's in negative time? Or behind the accepted starting position?
b. Find the average velocity of the object between 1 seconds and 4 seconds. Is this exact or approximate?
My guess: Uhm, well at 4 seconds the object appears to be moving at a rate of 5 meters per second, and if I had a function I would find the limit to prove this, but how can I do that without a function? At 1 second the object is moving at -0.7 meters per second? A.k.a going backwards? So the average speed would be 1.65 meters per second? I would say this is approximate.
c. For what times t is the object's velocity positive? For what times is the velocity negative?
My guess: Does this mean the intervals where the graph has a negative slope versus a positive slope? Or where the graph is above/below x=0?
