Question

Given the graph of the velocity of a particle from 0 to 9 seconds, on what interval is the particle moving to the right?left?Justify your answer.

Answer 1

I wrote that the particle is moving to the right on (0,1) and (5,7) since v ' (t)>0.
I wrote that the particle is moving to the left on (1,5) since v ' (t) <0.

Answer 2

Now I have to determine on what interval the particle is slowing down? speeding up? justify your answer. Not sure how to do this

Answer 3

It's almost perfect, except that the words v'(t) should have been v(t), since the graph is a velocity-time graph.
"I wrote that the particle is moving to the right on (0,1) and (5,7) since v ' (t)>0.
I wrote that the particle is moving to the left on (1,5) since v ' (t) <0."

Answer 4

The slope of a velocity-time graph represents the acceleration.
\(a(t)=\frac{dv}{dt}\)

Answer 5

Does that help?

Answer 6

Exactly, the sign of the velocity-time graph determines in which direction the particle is going. Good understanding of the concept!

Answer 7

yes, I see my jusifications were off because I was stating v ' (t) which is the acceleration and not the velocity

Answer 8

but I get stuck creating the second line, I need the acceleration to determine when the particle is slowing down or speeding up

Answer 9

I thought it was just a typo. But in math and physics, typos are not tolerated! :(

Answer 10

Recall that dv/dt is the acceleration, and dv/dt is also the slope of the velocity-time graph, namely the slopes of the lines, ignoring the vertices.
Can you find the slope of every line segment?

Answer 11

yes I can find the slope of every line segment give me a moment (please)

Answer 12

no problem, go ahead!