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?
To determine the position of the hockey puck at t = 10 s relative to its position at t = 0 s, we need to integrate the velocity function with respect to time over the interval [0, 10].
Looking at Figure 2-13, we see that the velocity of the puck is constant at v = -8 m/s from t = 0 s to t = 5 s, after which it jumps to v = -14 m/s and remains constant until t = 10 s.
To calculate the position, we can split the time interval into two parts:
1. From t = 0 s to t = 5 s: The velocity is constant at -8 m/s. Applying the formula for constant velocity motion, we have: Δx = v * Δt = (-8 m/s) * (5 s - 0 s) = -40 m.
2. From t = 5 s to t = 10 s: The velocity is constant at -14 m/s. Again, using the formula for constant velocity motion, we have: Δx = v * Δt = (-14 m/s) * (10 s - 5 s) = -70 m.
Adding up the displacements from each interval, we get the total displacement of the puck: -40 m + (-70 m) = -110 m.
Therefore, at t = 10 s, the hockey puck is positioned 110 meters behind its starting position at t = 0 s.