b. What is the total time for the jumper to slow down from 25m/s to zero? 6. A super tanker coming west into port started accelerating 2.0 hours before arriving. If the ship slowed at 25km/h^2 [E] before coming to a stop, what was the initial velocity?

**b. Calculating Time to Slow Down**<br /><br />Here's how to calculate the time it takes for the jumper to slow down:<br /><br />* **We need more information.** The problem only gives us the initial velocity (25 m/s) and the final velocity (0 m/s). To calculate the time, we also need the *acceleration* (or deceleration, which is just negative acceleration) experienced by the jumper. The formula we'd use is:<br /><br /> * v_f = v_i + at<br /><br /> Where:<br /> * v_f = final velocity (0 m/s)<br /> * v_i = initial velocity (25 m/s)<br /> * a = acceleration (which we need)<br /> * t = time (what we want to find)<br /><br />* **Example:** Let's say the jumper's deceleration is -2 m/s². Then the calculation would be:<br /><br /> * 0 = 25 + (-2)t<br /> * -25 = -2t<br /> * t = 12.5 seconds<br /><br />**6. Calculating Initial Velocity of Super Tanker**<br /><br />Here's how to calculate the initial velocity:<br /><br />* **Understand the problem:** The ship is decelerating eastward, which means its initial velocity was westward.<br /><br />* **Use the correct formula:** We can use the following kinematic equation:<br /><br /> * v_f = v_i + at<br /><br /> Where:<br /> * v_f = final velocity (0 km/h, since the ship comes to a stop)<br /> * v_i = initial velocity (what we want to find)<br /> * a = acceleration (-25 km/h² East, which is equivalent to +25 km/h² West since it's slowing down)<br /> * t = time (2.0 hours)<br /><br />* **Solve for v_i:**<br /><br /> * 0 = v_i + (25 km/h²)(2.0 h)<br /> * 0 = v_i + 50 km/h<br /> * v_i = -50 km/h<br /><br />* **Interpret the result:** The negative sign indicates the initial velocity was westward, as expected. Therefore, the initial velocity of the super tanker was **50 km/h [W]**.<br />