suppose that you drop the ball from a height of about 2m above the floor, releasing it from rest. on the axes that follow, sketch your predictions for the velocity-time and acceleration-time graphs of the ball's motion. assume that the positive y direction is upward
h = Vo*t + 0.5g*t^2 = 2 m.
0 + 4.9*t^2 = 2
t^2 = 0.4082
t = 0.639 s. = Fall time.
V = Vo + g*t = g*t. g = 10 m/s^2
Use the following points for graphing.
(t,v) = (0,0), (0.2,2), (0.3,3),(0.5,5),
(0.6,6).
To sketch the velocity-time and acceleration-time graphs for the ball's motion when it is dropped from a height of about 2m above the floor, we can utilize the following information:
1. Gravity: As the ball is dropped, it experiences a constant acceleration due to gravity, which is approximately 9.8 m/s² directed downward. Since the positive y direction is upward, the acceleration will be negative.
Now, let's break down both graphs:
1. Velocity-time graph:
- At the beginning, when the ball is dropped from rest, the velocity is zero.
- As the ball falls, the velocity increases. The slope of the graph will be positive, indicating a positive change in velocity.
- The velocity-time graph will be a straight line with a positive slope (representing increasing velocity) until the ball reaches its maximum velocity.
- At the maximum velocity, the velocity-time graph will plateau, indicating a constant velocity.
- Since the ball is dropping downward, the velocity will be negative on the graph.
2. Acceleration-time graph:
- The acceleration due to gravity is constant, so the graph will be a horizontal line.
- The acceleration-time graph will have a negative value, as the acceleration is directed downward.
- The graph will continue to be a straight line with a constant negative slope throughout the duration of the ball's fall.
Remember, during free fall, both the velocity and acceleration are negative due to the chosen positive y direction. So, both graphs will show negative values.
Please note that the precise shape and slope of the graphs will depend on the scale and units used on the axes.