How Do Cars A and B Interact on a Position-Time Graph?

[Toranc3]

Homework Statement

Two cars, A and B, move along the x-axis. Figure 2.39 is a graph of the positions of A and B versus time. (a) In motion diagrams (like Fig 2.13b and Fig 2.14b), show the position, velocity, and acceleration of each of the two cars at t=0, t=1s, and t=3s. (b) At what time(s) if any, do A and B have the same position? (c) Graph velocity versus time for both A and B. (d) At what time(s), if any, do A and B have the same velocity? (e) AT what time(s) if any, does car A pass car B? (f) At what time(s), if any does car B pass car A?

http://www.freeimagehosting.net/t/s9nhk.jpg

Homework Equations

The Attempt at a Solution

Part A:
http://www.freeimagehosting.net/t/f8rqy.jpg

Part B: At t=1s and 3s.

Part C: http://www.freeimagehosting.net/t/4m23n.jpg

Part D : I think at 1<x<3. Somewhere between there. Possibly at 2 seconds I think.

Part E: at 3 seconds car a passes car b.

Part F: After one second car b passes car a until they meet again at 3 seconds. Then car a passes car b.

Is this correct? Thanks in advance!

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[AdkinsJr]

For part B, the velocities are the derivatives for those curves. You need to consider when the slopes of the tangent lines to the curves your given for x vs. t are the same. In other words, when is the slope of the tangent line to A the same as the slope of line B?

Edit: I was rereading it, it's not clear what is meant by "velocity position." I thought it was asking when they have the same velocity, otherwise, you are correct, and D is correct.

 

[Toranc3]

For part B, the velocities are the derivatives for those curves. You need to consider when the slopes of the tangent lines to the curves your given for x vs. t are the same. In other words, when is the slope of the tangent line to A the same as the slope of line B?

Edit: I was rereading it, it's not clear what is meant by "velocity position." I thought it was asking when they have the same velocity, otherwise, you are correct, and D is correct.

Sorry but I fixed it now.