Question

A cross-country skier with an initial forward velocity of +4.42 m/s accelerates uniformly at 0.75 m/s^2. a. How long does it take the skier to come to a stop? b. What is the skier's displacement in this time interval?

Answer 1

The skier takes 5.89 seconds to come to a stop and has a displacement of 13.03 meters in this time interval.

Step-by-step explanation:

The skier's initial forward velocity is +4.42 m/s, and the acceleration is -0.75 m/s² (since it is in the opposite direction of the velocity). To determine how long it takes for the skier to come to a stop, we can use the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time taken. Plugging in the values, we have 0 = 4.42 + (-0.75)t. Solving for t, we get t = 5.89 seconds.

Now, to find the skier's displacement in this time interval, we can use the equation Δx = vit + 0.5at², where Δx is the displacement, vi is the initial velocity, t is the time taken, and a is the acceleration. Plugging in the values, we have Δx = (4.42)(5.89) + 0.5(-0.75)(5.89)². Simplifying the equation, we get Δx = 13.03 meters.