(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 11.3 m/s when going down a slope for 3.72 s? (b) How far does the skier travel in this time?
a. a = (11.3-0)/3.72 = 3.04 m/s^2.
b. d = 0.5*3.04*(3.72)^2 = 21.0 m.
To find the magnitude of the average acceleration of the skier, we can use the formula:
average acceleration = (final velocity - initial velocity) / time
(a) To find the magnitude of the average acceleration:
1. Identify the given information in the problem:
- Initial velocity (v0) = 0 m/s (since the skier starts from rest)
- Final velocity (v) = 11.3 m/s
- Time (t) = 3.72 s
2. Substitute the values into the formula:
average acceleration = (11.3 m/s - 0 m/s) / 3.72 s
3. Calculate the average acceleration:
average acceleration = 11.3 m/s / 3.72 s
(b) To find the distance traveled by the skier:
1. Use the formula for average velocity:
average velocity = total distance / total time
2. Rearrange the formula to solve for distance:
total distance = average velocity * total time
3. Substitute the values into the formula:
total distance = 11.3 m/s * 3.72 s
4. Calculate the distance:
total distance = 42.036 m
Therefore, (a) the magnitude of the average acceleration of the skier is approximately 3.04 m/s^2. (b) The skier travels approximately 42.036 meters in 3.72 seconds.