Motion along a line (Rectilinear Motion) Help

[Loppyfoot]

Alright, so I attached pictures of the problem from my textbook. I thought it would make it easier for you to help me.

I am having trouble picturing the velocity, acceleration and speed. If someone could help me through a, b, c, and d, I would love the help.

Thanks

 

[Loppyfoot]

Anyone available to help?

 

[Mark44]

a. The particle is moving right if the position (x value) is increasing, and moving to the left if the position is decreasing.

When the tangent to the graph of x(t) is horizontal, the particle is stopped. Can you sketch a rough graph of the velocity v(t) of the particle? You can do this by estimating the slope of the tangent line at a few points and plotting those values.

The acceleration a(t) is the derivative of the velocity. If you have a graph of the velocity, you can estimate the slope of the tangent line at a few points, and graphing them.