A stone is thrown straight up at 8.99 m/s. What is the stone's acceleration in m/s/s at the top of its rise?
To find the stone's acceleration at the top of its rise, we need to understand the motion of the stone. When the stone is thrown straight up, it experiences a constant force due to gravity pulling it down towards the Earth. This force causes the stone to decelerate as it moves upward, eventually coming to a stop at the highest point before reversing direction and falling back down.
At the top of its rise, the stone momentarily stops moving before it starts falling back down. At this point, its velocity is zero.
To find the stone's acceleration at the top, we can use the formula for acceleration:
acceleration = change in velocity / change in time
Since the stone's velocity is 8.99 m/s when it is thrown up and becomes 0 m/s at the top, the change in velocity is 0 - 8.99 = -8.99 m/s.
However, we need to determine the time it takes for the stone to reach the top. To do this, we can use the equation for the time it takes for an object to reach its maximum height:
time = (final velocity - initial velocity) / acceleration
In this case, the final velocity is 0 m/s, the initial velocity is 8.99 m/s, and the acceleration is due to gravity, which is approximately -9.8 m/s^2 (negative because it acts in the opposite direction to the positive direction we chose).
Substituting the values into the equation, we get:
time = (0 - 8.99) / -9.8
Simplifying, we have:
time = 0.9188 seconds
Now that we know the time it takes for the stone to reach the top, we can calculate the stone's acceleration at that point using the formula mentioned earlier:
acceleration = change in velocity / change in time
The change in velocity is again -8.99 m/s (from 8.99 m/s to 0 m/s), and the change in time is 0.9188 seconds.
Substituting the values, we get:
acceleration = -8.99 / 0.9188 ≈ -9.79 m/s^2
Therefore, the stone's acceleration at the top of its rise is approximately -9.79 m/s^2. Note that the negative sign indicates that the acceleration is directed downwards, opposite to the direction of the stone's motion.