A Skier's Acceleration Down a Slope

When will the skier acquire a speed of 24 m/s after starting from rest and sliding 9m down a slope in 3sec?

Final Answer:

It will take 0.75 seconds for the skier to acquire a speed of 24 m/s.

Explanation:

To find the time it takes for the skier to reach a speed of 24 m/s, we can use the equations of motion. By rearranging the equations and substituting the given values, we find that it will take 0.75 seconds. To calculate the time, we can use the equation: final velocity = initial velocity + acceleration * time. Since the skier starts from rest, the initial velocity is 0 m/s. With constant acceleration, we can rearrange the equation to find the time: time = (final velocity - initial velocity) / acceleration. Substituting the values, we get: time = (24 m/s - 0 m/s) / acceleration. To find the acceleration, we use the kinematic equation: final velocity^2 = initial velocity^2 + 2 * acceleration * distance. Since the skier starts from rest, the initial velocity is 0 m/s. Rearranging the equation to solve for acceleration, we get: acceleration = (final velocity^2) / (2 * distance). Substituting the values, we find: acceleration = (24 m/s)^2 / (2 * 9 m). Substituting the acceleration back into the equation for time, we have: time = (24 m/s - 0 m/s) / ((24 m/s)^2 / (2 * 9 m)). Simplifying further, we find the skier will acquire a speed of 24 m/s after 0.75 seconds.

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