A child sleds down a snow covered hill with a uniform acceleration. The slope of the hill is 38.5 m long. If the child starts at rest and reaches the bottom of the hill in 5.5 s, what is the child's final speed?
To find the child's final speed, we can use the kinematic equation:
v = u + at
where:
v = final velocity (speed)
u = initial velocity (0 m/s, as the child starts at rest)
a = acceleration
t = time (5.5 s)
First, we need to find the acceleration. We know that the acceleration is uniform, so we can use the equation:
s = ut + (1/2)at^2
where:
s = distance (length of the hill, 38.5 m)
u = initial velocity (0 m/s)
t = time (5.5 s)
Plugging in the values, we get:
38.5 = (1/2)a * (5.5^2)
Simplifying:
38.5 = 15.125a
Now, we can solve for the acceleration:
a = 38.5 / 15.125
a ≈ 2.54 m/s^2
Now, we can use the equation for final velocity:
v = u + at
Plugging in the values:
v = 0 + (2.54)(5.5)
v ≈ 13.97 m/s
Therefore, the child's final speed is approximately 13.97 m/s.
To solve this problem, we can use the kinematic equation that relates the final speed (vf), initial speed (vi), acceleration (a), and distance (d):
vf^2 = vi^2 + 2ad
In this case, the child starts at rest (vi = 0), the distance is the length of the hill (d = 38.5 m), and we are given the time it takes to reach the bottom (t = 5.5 s).
First, let's find the acceleration (a).
The formula to calculate acceleration is:
a = (vf - vi) / t
Since the child starts at rest, vi = 0, so the acceleration simplifies to:
a = vf / t
Now, plug in the values we have:
a = vf / 5.5 s
To find the final speed (vf), let's rearrange the equation:
vf = a * t
Substitute the value of acceleration we found:
vf = (vf / 5.5 s) * 5.5 s
Simplifying the equation, we find:
vf = vf
Since the same value for vf appears on both sides of the equation, it means that vf can have any value. This implies that the final speed of the child can be any value, depending on the acceleration of the sled.
Therefore, we cannot determine the final speed of the child based on the given information.