Question

Below is the graph of the velocity of an object moving in the positive direction along the x-axis. Answer the following questions using only the information from the graph.
A) Find a time t when the object changes directions. If this never happens say "this never happens." Explain your answer.
B) Find the time when the object is furthest to the right. Explain your answer.
C) What is the object's maximum acceleration? Explain how you found this.
D) What is the object's maximum speed? At what time(s) does it reach its maximum speed?

Answer 1

HI!!

Answer 2

it changes direction when the velocity goes from being negative to positive or positive to negative

Answer 3

Okay. I'm pretty comfortable with A and B. What I am really having a hard time with is visualizing C and D.

Answer 4

it's maximum acceleration is when the slope is most steep

Answer 5

Acceleration is the derivative of velocity, and the steepness of slopes tells you the magnitude of acceleration.

Answer 6

As for maximum velocity, that is simply the peaks of velocity.

Answer 7

Okay I understand where the highest acceleration is now. But what about the highest speed? Would that occur at x=3?

Answer 8

Yeah, but I think you mean \(t\)

Answer 9

yes, my bad

Answer 10

Thanks for the help. I think I figure it out.