(a)What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.61 m/s when going down a slope for 1.84 s? How far does the skier travel in this time?
To find the magnitude of the average acceleration of the skier, we can use the following equation:
average acceleration = (final velocity - initial velocity) / time
Given:
initial velocity (u) = 0 m/s (starting from rest)
final velocity (v) = 8.61 m/s
time (t) = 1.84 s
average acceleration = (8.61 m/s - 0 m/s) / 1.84 s
average acceleration = 8.61 m/s / 1.84 s
average acceleration ≈ 4.68 m/s² (rounded to two decimal places)
To find the distance traveled by the skier, we can use the formula:
distance = (initial velocity * time) + (0.5 * average acceleration * time²)
distance = (0 m/s * 1.84 s) + (0.5 * 4.68 m/s² * (1.84 s)²)
distance = 0 m + 0.5 * 4.68 m/s² * 3.3856 s²
distance = 0 + 0.5 * 4.68 m/s² * 3.3856 s²
distance ≈ 0 + 0.5 * 4.68 m/s² * 11.4656 m²
distance ≈ 0 + 25.834048 m³/s²
distance ≈ 25.83 m (rounded to two decimal places)
Therefore, the magnitude of the average acceleration of the skier is approximately 4.68 m/s², and the skier travels approximately 25.83 meters in 1.84 seconds.