On a dare, you decide to try bungee jumping. You fall freely you are moving at 15 m/s downward. At that point the cord begins to stretch. The cord slows you to a stop as it stretches, then pulls you back upwards. When the cord is no longer pulling on you, you are moving upwards at 8 m/s. The time between moving at 15 m/s downward and moving 8 m/s upward is 3 seconds. Draw a motion diagram for this situation. What is your acceleration as the bungee cord changes your direction? What is the direction of that acceleration?

To draw a motion diagram for this situation, we can break the motion into three phases: the initial free fall, the deceleration, and the upward acceleration.

Phase 1: Free Fall
During free fall, you are moving downward at a constant speed of 15 m/s. We can represent this phase with an arrow pointing straight down labeled as 15 m/s.

Phase 2: Deceleration
The cord begins to stretch and decelerates your downward motion until you come to a stop before changing direction. This phase lasts for 3 seconds. We can represent this phase with a set of arrows getting shorter and shorter until they become 0 m/s.

Phase 3: Upward Acceleration
Once the cord has stretched to its maximum, it starts to pull you upwards, causing you to accelerate. You move upward at a speed of 8 m/s. We can represent this phase with an arrow pointing straight up labeled as 8 m/s.

Now, let's move on to calculating the acceleration and its direction.

Acceleration is defined as the rate of change of velocity. To find the acceleration during the deceleration phase, we can use the formula:

acceleration = (change in velocity) / (change in time)

In this case, the change in velocity is from 15 m/s to 0 m/s, and the change in time is 3 seconds. Substituting these values into the formula, we get:

acceleration = (0 m/s - 15 m/s) / (3 s)
acceleration = -15 m/s / 3 s
acceleration = -5 m/s²

So, the acceleration during the deceleration phase is -5 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial motion, which is downward.

During the upward acceleration phase, the acceleration can be calculated using the same formula but with the change in velocity from 0 m/s to 8 m/s and the time of 3 seconds:

acceleration = (8 m/s - 0 m/s) / (3 s)
acceleration = 8 m/s / 3 s
acceleration = 2.67 m/s²

Thus, the acceleration during the upward acceleration phase is 2.67 m/s² and its direction is upward, opposite to the initial direction of motion.

So, the acceleration as the bungee cord changes your direction is -5 m/s² during the deceleration phase (downward), and 2.67 m/s² during the upward acceleration phase (upward).