(a) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 9.62 m/s when going down a slope for 4.00 s? (b) How far does the skier travel in this time?
a = change in velocity/change in time
= 9.62/4
average speed = 9.62/2 = 4.81
distance = 4 * 4.81
To find the magnitude of the average acceleration of the skier, we can use the equation for average acceleration:
Average acceleration = (final velocity - initial velocity) / time
In this case, the skier starts from rest, so the initial velocity is 0 m/s. The final velocity is given as 9.62 m/s, and the time is given as 4.00 s. Therefore, we can substitute these values into the equation:
Average acceleration = (9.62 m/s - 0 m/s) / 4.00 s
Simplifying this, we get:
Average acceleration = 9.62 m/s / 4.00 s
Now, we can divide the numerator by the denominator:
Average acceleration = 2.405 m/s^2
So, the magnitude of the average acceleration of the skier is 2.405 m/s^2.
To determine how far the skier travels in this time, we can use the equation for distance traveled with constant acceleration:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the initial velocity is 0 m/s, the time is 4.00 s, and the average acceleration is 2.405 m/s^2 (as calculated above). Substituting these values into the equation, we get:
Distance = (0 m/s * 4.00 s) + (0.5 * 2.405 m/s^2 * (4.00 s)^2)
Simplifying this, we have:
Distance = 0 m + 0.5 * 2.405 m/s^2 * 16.00 s^2
Now, we multiply the numbers and units to get the final result:
Distance = 0 m + 19.240 m
So, the skier travels a distance of 19.240 meters in this time.