2. A baseball starts from rest and rolls 50.0 m down a hill in 10.0 seconds.
What is the acceleration?
distance = 1/2 * acceleration * (time)^2
To find the acceleration, we can use the formula:
acceleration (a) = (final velocity - initial velocity) / time
In this case, the baseball starts from rest, which means the initial velocity (u) is 0 m/s. The final velocity (v) can be calculated using the formula:
final velocity (v) = initial velocity + (acceleration * time)
Since the baseball rolls down the hill, we can assume that the acceleration due to gravity (g) is acting on it. The value of acceleration due to gravity is approximately 9.8 m/s^2.
Plugging the given values into the formula, we get:
v = 0 + (9.8 m/s^2 * 10.0 s)
v = 98 m/s
Now we have the final velocity, we can calculate the acceleration:
a = (98 m/s - 0 m/s) / 10.0 s
a = 9.8 m/s^2
The acceleration of the baseball rolling down the hill is 9.8 m/s^2.
To find the acceleration, we can use the formula for acceleration:
acceleration = change in velocity / time
In this case, the baseball starts from rest, so its initial velocity (u) is 0 m/s. The final velocity (v) can be calculated using the formula:
v = u + at
Where:
u = initial velocity (0 m/s)
a = acceleration
t = time (10.0 seconds)
Since the baseball rolls down a hill, we can assume that it accelerates only in one direction, which we can take as positive. Therefore, the displacement (s) is given as -50.0 m (negative because it is in the opposite direction).
Using the formula for displacement:
s = ut + (1/2)at^2
We can rearrange this equation to find the value of a:
a = 2(s - ut) / t^2
Plugging in the given values:
a = 2(-50.0 - (0)(10.0))/(10.0)^2
a = -1 m/s^2
Therefore, the acceleration of the baseball is -1 m/s^2.