Assumptions:
* Neglecting air resistance: For simplicity, we'll assume there's no air resistance affecting the ball's motion.
* Constant gravitational acceleration: We'll assume the acceleration due to gravity (g) is constant at approximately 9.8 m/s².
Scenario:
Let's consider a ball thrown vertically upwards with an initial velocity (v₀).
Analysis:
1. Upward motion:
* As the ball travels upwards, gravity acts against its motion, causing it to slow down.
* The velocity decreases linearly with time.
* The equation for velocity (v) at any time (t) during the upward motion is:
* v = v₀ - gt
2. Maximum height:
* At the maximum height, the ball momentarily comes to rest.
* The velocity becomes zero (v = 0).
3. Downward motion:
* As the ball falls back down, gravity now acts in the same direction as its motion, causing it to speed up.
* The velocity increases linearly with time.
* The equation for velocity (v) at any time (t) during the downward motion is:
* v = gt
Graph:
The graph of velocity vs. time would look like this:
* Shape: A V-shape.
* Slope: The slope of the lines represents the acceleration due to gravity (g).
* Intercept: The y-intercept represents the initial velocity (v₀).
Key Points:
* The velocity is positive during the upward motion and negative during the downward motion (assuming upward direction as positive).
* The magnitude of the velocity is the same at the same height above and below the maximum height.
Example:
If a ball is thrown upwards with an initial velocity of 20 m/s, its velocity after 1 second would be:
* v = v₀ - gt = 20 m/s - 9.8 m/s² * 1 s = 10.2 m/s (upwards)
After 2 seconds, the velocity would be:
* v = v₀ - gt = 20 m/s - 9.8 m/s² * 2 s = 0.4 m/s (upwards)
And after 3 seconds, the velocity would be:
* v = v₀ - gt = 20 m/s - 9.8 m/s² * 3 s = -9.4 m/s (downwards)
Conclusion:
The velocity of a vertically thrown ball varies linearly with time, changing direction at the maximum height. The rate of change in velocity is determined by the acceleration due to gravity.
