An object travels with a constant acceleration for 10 s. The vectors in Figure 3-41 represent the final and initial velocities. carefully graph the x component of the velocity versus time, the y component of the velocity versus time and the y component of the acceleration versus time.

Sure, let me give you a carefully graphed response... Just kidding! As a text-based bot, I can't provide an actual graph. But I can definitely help you understand the concept!

To graph the x-component of velocity versus time, you'll need to know the initial and final velocities in the x-direction, as well as the acceleration. From there, you can use the equation:

Vx = Vx0 + a*t

where Vx is the x-component of velocity, Vx0 is the initial velocity, a is the acceleration, and t is time. By plugging in the values at various time intervals, you can plot the graph.

For the y-component of velocity versus time, you can use the same equation but with the y-direction values.

To graph the y-component of acceleration versus time, you'll need the y-component of the acceleration at various time intervals. You can calculate this by using the equation:

ay = (Vy - Vy0) / t

where ay is the y-component of acceleration, Vy is the final velocity in the y-direction, Vy0 is the initial velocity in the y-direction, and t is time.

Remember, these graphs will depend on the specific values of the initial and final velocities, as well as the acceleration. So, be cautious and double-check your values before plotting the graphs!

To carefully graph the x component of the velocity versus time, y component of the velocity versus time, and y component of the acceleration versus time, you will need certain information that is not provided in the question, such as the initial and final velocities, and the acceleration.

However, I can explain the general procedure to graph these quantities:

1. Identify the given vectors in Figure 3-41: the final and initial velocities.

2. Determine the initial and final values of the x and y components of the velocities from the given vectors.

3. Calculate the acceleration by finding the change in velocity with respect to time. If the acceleration is constant, the change in velocity is given by:

Δv = vf - vi,

where Δv is the change in velocity, vf is the final velocity, and vi is the initial velocity.

Assuming the acceleration is constant, you can use the formula:

a = Δv / t,

where a is the acceleration, Δv is the change in velocity, and t is the time interval.

4. Based on the values obtained, choose a suitable scale for the time axis.

5. On the x component of velocity versus time graph, plot the x component of the velocity as a function of time. The x component of velocity remains constant as per the given information, so it will simply be a horizontal line.

6. On the y component of velocity versus time graph, plot the y component of the velocity as a function of time. The y component of the velocity may change with time, so it will not be a horizontal line.

7. On the y component of acceleration versus time graph, plot the y component of the acceleration as a function of time. Since the object is said to have constant acceleration, the y component of the acceleration will also be constant and can be represented as a horizontal line.

Remember to label the axes appropriately and include units, if provided.

Note: Without specific information about the initial and final velocities, as well as the acceleration, it is impossible to provide an exact graph.