At time t = 0, a hockey puck is sent sliding in the +x direction over a frozen lake, directly into a strong wind. Figure 2-13 gives the velocity v of the puck versus time, as the puck moves along a single axis. (The time axis is marked in increments of 1.0 s.) At t = 10. s, what is its position relative to its position x = 0 at t = 0?

thanks!

Henry hits a hockey puck in the positive

x-direction at time, t ≈ t0. The puck is then
stopped by a net starting at time, t ≈ t1.
Which of the following curves could describe
the acceleration of the hockey puck if
we ignore any effects of friction?

To determine the position of the hockey puck at t = 10.0 s, we can use the velocity-time graph given in Figure 2-13.

In the graph, the velocity v of the puck is plotted on the y-axis, and time t is plotted on the x-axis. To find the position of the puck at a specific time, we need to calculate the area under the velocity-time graph up to that time.

Given that the velocity is constant between each plotted point, we can approximate the area under the graph as a series of rectangles.

First, let's divide the graph into intervals of 1.0 s based on the time increments marked on the x-axis.

Looking at the graph, we can see that the velocity is negative (i.e., the puck is moving in the -x direction) for the first 4 seconds, and then it becomes positive (moving in the +x direction) for the next 6 seconds.

To calculate the position of the puck at t = 10.0 s, we can calculate the area under each segment separately.

Segment 1:
Area = time interval * velocity
Area = 4 s * (-4 m/s) = -16 m
(Note: The negative area indicates that the puck is moving in the opposite direction of the positive x-axis.)

Segment 2:
Area = time interval * velocity
Area = 6 s * (6 m/s) = 36 m

Now we can calculate the total position of the puck by summing the areas under both segments:

Total position = Area of segment 1 + Area of segment 2
Total position = -16 m + 36 m = 20 m

So, at t = 10.0 s, the hockey puck is located 20 meters to the +x direction relative to its initial position at t = 0.