What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.0 m/s when going down a slope for 5.0 s? How far does the skier travel in this time?
a = change in speed/ change in time
= (8-0)/5 = 1.6 m/s^2
d = (1/2) a t^2 = .5*1.6*25 = 20 meters
or alternatively
average speed = 4 m/s * 5 s = 20 meters
To find the magnitude of the average acceleration of the skier, we can use the formula:
average acceleration = change in velocity / change in time
In this case, the change in velocity is given by the final velocity (8.0 m/s) minus the initial velocity (0 m/s) since the skier starts from rest.
So, change in velocity = 8.0 m/s - 0 m/s = 8.0 m/s
The change in time is given as 5.0 s.
Now we can calculate the average acceleration:
average acceleration = change in velocity / change in time
= 8.0 m/s / 5.0 s
= 1.6 m/s²
So, the magnitude of the average acceleration of the skier is 1.6 m/s².
To find the distance traveled by the skier in this time, we can use the equation:
distance = initial velocity × time + 0.5 × acceleration × time²
Since the skier starts from rest, the initial velocity is 0 m/s.
distance = 0 m/s × 5.0 s + 0.5 × 1.6 m/s² × (5.0 s)²
= 0 + 0.5 × 1.6 m/s² × 25 s²
= 0 + 0.5 × 1.6 m/s² × 25 s²
= 0 + 20 m
= 20 m
Therefore, the skier travels a distance of 20 meters in 5.0 seconds.