(a) To determine the magnitude of the initial velocity of the ball, we need to find the value of the velocity when time is equal to 0. From the graph, we can see that at t = 0, the velocity is approximately 6 m/s. Therefore, the magnitude of the initial velocity of the ball is 6 m/s.
(b) To calculate the distance traveled by the ball during 20 seconds, we need to find the area under the velocity-time graph for the given time interval. From the graph, we can see that the graph is a triangle. The formula to calculate the area of a triangle is:
Area = (base * height) / 2
In this case, the base of the triangle is 20 seconds, and the height is 6 m/s. Plugging in these values into the formula, we get:
Area = (20 * 6) / 2 = 60 meters
Therefore, the distance traveled by the ball during 20 seconds is 60 meters.
(c) To calculate the acceleration of the ball from the graph, we need to find the slope of the velocity-time graph. Since the graph is a straight line, the slope represents the acceleration.
From the graph, we can see that the slope of the line is constant and equal to -2 m/s^2. Therefore, the acceleration of the ball is -2 m/s^2.